Gravitation
85 JEE Physics previous year questions on Gravitation — options free on every question; 8 include the answer & explanation free, the rest unlock with PYQ Pass.
The mass of the moon is \(\frac{1}{144}\) times the mass of a planet and its diameter is \(\frac{1}{16}\) times the diameter of a planet. If the escape velocity on the planet is \(v\), the escape velocity on the moon will be :
[JEE Main 2024, 31 Jan (Shift 2)]
\(\frac{v}{3}\)
The formula for escape velocity is:
\[v = \sqrt{\frac{2GM}{R}}\]From the given problem, the ratios for the moon compared to the planet are:
Mass: \({M}_{m}=\frac{{M}_{p}}{144}\)
Radius: \({R}_{m}=\frac{{R}_{p}}{16}\) (the ratio of radii is the same as the ratio of diameters)
Now, we can find the escape velocity on the moon (\({v}_{m}\)) by setting up a ratio:
\[\frac{v_m}{v_p} = \sqrt{\frac{M_m}{M_p} \times \frac{R_p}{R_m}}\]Substitute the given values:
\[\frac{v_m}{v} = \sqrt{\frac{1}{144} \times 16}\] \[\frac{v_m}{v} = \sqrt{\frac{16}{144}}\] \[\frac{v_m}{v} = \sqrt{\frac{1}{9}}\] \[\frac{v_m}{v} = \frac{1}{3}\] \[v_m = \frac{v}{3}\]Correct Option: D
The mass of the moon is \(\frac{1}{144}\) times the mass of a planet and its diameter is \(\frac{1}{16}\) times the diameter of a planet. If the escape velocity on the planet is \(v\), the escape velocity on the moon will be :
[JEE Main 2024, 31 Jan (Shift 2)]
\(\frac{v}{3}\)
The formula for escape velocity is:
\[v = \sqrt{\frac{2GM}{R}}\]From the given problem, the ratios for the moon compared to the planet are:
Mass: \({M}_{m}=\frac{{M}_{p}}{144}\)
Radius: \({R}_{m}=\frac{{R}_{p}}{16}\) (the ratio of radii is the same as the ratio of diameters)
Now, we can find the escape velocity on the moon (\({v}_{m}\)) by setting up a ratio:
\[\frac{v_m}{v_p} = \sqrt{\frac{M_m}{M_p} \times \frac{R_p}{R_m}}\]Substitute the given values:
\[\frac{v_m}{v} = \sqrt{\frac{1}{144} \times 16}\] \[\frac{v_m}{v} = \sqrt{\frac{16}{144}}\] \[\frac{v_m}{v} = \sqrt{\frac{1}{9}}\] \[\frac{v_m}{v} = \frac{1}{3}\] \[v_m = \frac{v}{3}\]Correct Option: D
Assuming the earth to be a sphere of uniform mass density, a body weighed \(300 \ N\) on the surface of earth. How much it would weigh at \(\frac{R}{4}\) depth under surface of earth ?
\(225 \ N\)
For a uniform-density Earth, acceleration due to gravity at a depth d is
g_d=g\left(1-\frac{d}{R}\right)
Given:
\(d=\frac{R}{4}\)
Therefore,
\({g}_{d}=g(1-\frac{1}{4})\) \({g}_{d}=\frac{3}{4}g\)
Weight is proportional to g.
\({W}_{d}=300\times \frac{3}{4}\) \({W}_{d}=225\ \text{N}\)
A planet \(\left({P}_{1}\right)\) is moving around the star of mass 2M in the orbit of radius R. Another planet \(\left({P}_{2}\right)\) is moving around another star of mass 4 M in a orbit of radius 2 R . Ratio of time periods of revolution of \({P}_{2}\) and \({P}_{1}\) is_________
[JEE Main 2026, 2 Apr (Shift 1)]
2
Using Kepler’s third law:
\(T\propto \frac{{R}^{3/2}}{\sqrt{M}}\)
For \({P}_{1}:{T}_{1}\propto \frac{{R}^{3/2}}{\sqrt{2M}}\)
For \({P}_{2}:{T}_{2}\propto \frac{(2R{)}^{3/2}}{\sqrt{4M}}=\frac{\sqrt{2}{R}^{3/2}}{\sqrt{M}}\)
Ratio: \(\frac{{T}_{2}}{{T}_{1}}=\frac{\sqrt{2}/\sqrt{M}}{1/\sqrt{2M}}=2\)
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant.
Reason (R) : For a central force field the angular momentum is a constant.
In the light of the above statements, choose the most appropriate answer from the options given below :
[JEE Main 2025, 7 Apr (Shift 2)]
Both (A) and (R) are correct and (R) is the correct explanation of (A)
\(\frac{dA}{dt}=\frac{L}{2m}\)
Due to central force torque is zero & angular momentum is constant.
In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of :
[JEE Main 2024, 5 Apr (Shift 1)]
\({10}^{39}\)
key concept= Columb's low + Law of gravitation
\({F}_{e}=\frac{k{r}_{1}{r}_{2}}{{r}^{2}}=\frac{9\times {10}^{9}\times {\left(1.6\times {10}^{-19}\right)}^{2}}{{r}^{2}}\)
\({F}_{g}=\frac{G{m}_{1}{m}_{2}}{{r}^{2}}=\frac{6.67\times {10}^{-11}\times 9.1\times {10}^{-31}\times 1.67\times {10}^{-27}}{{r}^{2}}\)
\(∴\frac{{\mathrm{F}}_{\mathrm{e}}}{{\mathrm{F}}_{\mathrm{g}}}=2.2\times {10}^{39}\)
Consider a star of mass \(m_2 kg\) revolving in a circular orbit around another star of mass \(m_1 kg\) with \(m_1 \gg m_2\). The heavier star slowly acquires mass from the lighter star at a constant rate of \(\gamma kg / s\). In this transfer process, there is no other loss of mass. If the separation between the centers of the stars is \(r\), then its relative rate of change \(\frac{1}{r} \frac{d r}{d t}\) (in \(s ^{-1}\) ) is given by:
[JEE Advanced 2025]
\(-\frac{2\gamma }{{m}_{2}}\)
- System: Binary star system with masses \({m}_{1}\)and\({m}_{2}\) (\({m}_{1}≫{m}_{2}\)).
- Process: Mass transfer from lighter star (\({m}_{2}\)) to heavier star (\({m}_{1}\)) at a rate \(\gamma\).
- \({\overset{˙}{m}}_{1}=\gamma\)
- \({\overset{˙}{m}}_{2}=−\gamma\)
- Total mass \(M={m}_{1}+{m}_{2}\)is constant.
- Principle: Conservation of orbital angular momentum \(L\).
Step 1: Write the expression for Angular Momentum. The orbital angular momentum \(L\) for a binary system is given by: \(L=\mu \sqrt{GMr}\) where \(\mu =\frac{{m}_{1}{m}_{2}}{{m}_{1}+{m}_{2}}\) is the reduced mass, \(M\) is the total mass, and \(r\) is the separation.
Step 2: Differentiate with respect to time. Taking the natural logarithm of both sides: \(\text{ln}L=\text{ln}\mu +\frac{1}{2}\text{ln}\left(GM\right)+\frac{1}{2}\text{ln}r\) Since \(L\),\(G\), and \(M\) are constant, their derivatives are zero. Differentiating with respect to time \(t\) : \(0=\frac{1}{\mu }\frac{d\mu }{dt}+\frac{1}{2r}\frac{dr}{dt}\)Rearranging to solve for the relative rate of change of r : \(\frac{1}{r}\frac{dr}{dt}=−2\frac{1}{\mu }\frac{d\mu }{dt}\)
Step 3: Calculate \(\frac{1}{\mu }\frac{d\mu }{dt}\). Using the definition of reduced mass \(\mu =\frac{{m}_{1}{m}_{2}}{M}\): \(\text{ln}\mu =\text{ln}{m}_{1}+\text{ln}{m}_{2}−\text{ln}M\) \(\frac{1}{\mu }\frac{d\mu }{dt}=\frac{{\overset{˙}{m}}_{1}}{{m}_{1}}+\frac{{\overset{˙}{m}}_{2}}{{m}_{2}}\)Substitute \({\overset{˙}{m}}_{1}=\gamma\) and \({\overset{˙}{m}}_{2}=−\gamma\): \(\frac{1}{\mu }\frac{d\mu }{dt}=\frac{\gamma }{{m}_{1}}−\frac{\gamma }{{m}_{2}}=\gamma \left(\frac{1}{{m}_{1}}−\frac{1}{{m}_{2}}\right)\)
Step 4: Apply the approximation \({m}_{1}≫{m}_{2}\). Since \({m}_{1}\) is much larger than \({m}_{2}\), the term \(\frac{1}{{m}_{1}}\)is negligible compared to \(\frac{1}{{m}_{2}}.\frac{1}{\mu }\frac{d\mu }{dt}\approx \gamma \left(0−\frac{1}{{m}_{2}}\right)=−\frac{\gamma }{{m}_{2}}\)
Step 5: Final Result. Substitute this back into the equation for \(\frac{1}{r}\frac{dr}{dt}:\frac{1}{r}\frac{dr}{dt}=−2\left(−\frac{\gamma }{{m}_{2}}\right)=\frac{2\gamma }{{m}_{2}}\)
Note: While the derived physical result is positive (indicating orbit expansion), the options provided in the question all have a negative sign. This suggests a sign convention difference or a typo in the question statement regarding the direction of mass flow (usually Heavy \(\to\) Light causes shrinking/negative rate). However, the magnitude and dependency on \({m}_{2}\) clearly point to Option (B).
Answer: (B) \(−\frac{2\gamma }{{m}_{2}}\)
A particle of mass m is under the influence of the gravitational field of a body of mass M(≫ m). The particle is moving in a circular orbit of radius r0 with time period T0 around the mass M. Then, the particle is subjected to an additional central force, corresponding to the potential energy Vc(r) = mα/r3, where α is a positive constant of suitable dimensions and r is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius r0 in the combined gravitational potential due to M and Vc(r), but with a new time period T1, then\(\left({\mathrm{T}}_{1}^{2}-{\mathrm{T}}_{0}^{2}/{\mathrm{T}}_{1}^{2}\right)\) is given by
[G is the gravitational constant.]
\(\frac{3\alpha }{{\mathrm{GMr}}_{0}^{2}}\)
\(\frac{\mathrm{GMm}}{{\mathrm{r}}_{0}^{2}}={\mathrm{mω}}^{2}{\mathrm{r}}_{0}\)
\(\omega =\sqrt{\frac{\mathrm{GM}}{{\mathrm{r}}_{0}^{3}}}\)
\({\mathrm{T}}_{0}^{2}=4{\pi }^{2}(\frac{{\mathrm{r}}_{0}^{3}}{\mathrm{GM}})\) .....(1)
\(\mathrm{F}=−\frac{{\mathrm{dv}}_{\mathrm{c}}(\mathrm{r})}{\mathrm{dr}}\)
\(\mathrm{F}=\frac{3\mathrm{mα}}{{\mathrm{r}}^{4}}\)
Net force
\(\frac{\mathrm{GMm}}{{\mathrm{r}}_{0}^{2}}−\frac{3\mathrm{mα}}{{\mathrm{r}}_{0}^{4}}={\mathrm{mω}}^{2}{\mathrm{r}}_{0}\)
\({\omega }^{2}=\frac{\mathrm{GM}}{{\mathrm{r}}_{0}^{3}}−\frac{3\alpha }{{\mathrm{r}}_{0}^{5}}\)
We know \(\omega =\frac{2\pi }{{\mathrm{T}}_{1}}\)
\(\frac{4{\pi }^{2}}{{\mathrm{T}}_{1}^{2}}=\frac{\mathrm{GM}}{{\mathrm{r}}_{0}^{3}}−\frac{3\alpha }{{\mathrm{r}}_{0}^{5}}\)
\({\mathrm{T}}_{1}^{2}=\frac{4{\pi }^{2}}{\frac{\mathrm{GM}}{{\mathrm{r}}_{0}^{3}}−\frac{3\alpha }{{\mathrm{r}}_{0}^{5}}}\) ......(2)
From equation (1) and (2)
\(\frac{{\mathrm{T}}_{1}^{2}−{\mathrm{T}}_{0}^{2}}{{\mathrm{T}}_{1}^{2}}=\frac{3\alpha }{{\mathrm{GMr}}_{0}^{2}}\)
A body of mass m is taken from Earth's surface to a height equal to twice the radius of Earth (Rₑ). The increase in potential energy will be:
[JEE Main 2026, 5 Apr (Shift 2)]
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The height in terms of radius of the earth \((\mathrm{R})\), at which the acceleration due to gravity becomes \(\frac{g}{9}\) where \(g\) is acceleration due to gravity on earth's surface, is _______ .
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When one moves from a point 16 km below the earth's surface to a point 16 km above the earth's surface, the change in g is approximately α%. The value of α is____.
(Take radius of the earth = 6400 km):
[JEE Main 2026, 5 Apr (Shift 1)]
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Satellite A is launched into a circular orbit of radius R. Satellite B is launched into a circular orbit of radius 1.03R. By approximately what percentage is the time period of B greater than that of A?
(Shift I - Memory Based)
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Two planet A and B are revolving around a massive star such that \(r_A=2 r_B\) and \(m_A=4 \sqrt{3} m_B\). Find ratio of angular momentum of planet B to planet A.(Shift - II Memory Based)
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A satellite is launched into a circular orbit of radius ' R ' around the earth. A second satellite is launched into an orbit of radius 1.03 R . The time period of revolution of the second satellite is larger than the first one approximately by.
[JEE Main 2025, 24 Jan (Shift 1)]
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If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon is 27 days and gravitational attraction between the satellite and the moon is neglected.
[JEE Main 2025, 23 Jan (Shift 2)]
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If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon =27 days and gravitational attraction between the satellite and the moon is neglected.
[JEE Main 2025, 23 Jan (Shift 2)]
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The escape velocity from the surface of the Earth is \(11.2 \mathrm{~km} / \mathrm{s}\). Find the escape velocity from a planet whose radius is 2 times that of Earth and mass is 8 times that of Earth.
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Consider a star of mass \(m_2 \ kg\) revolving in a circular orbit around another star of mass \(m_1 \ kg\) with \(m_1 \gg m_2\). The heavier star slowly acquires mass from the lighter star at a constant rate of \(\gamma \ kg / s\). In this transfer process, there is no other loss of mass. If the separation between the centers of the stars is \(r\), then its relative rate of change \(\frac{1}{r} \frac{d r}{d t}\) (in \(s ^{-1}\) ) is given by:
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A particle of mass m is under the influence of the gravitational field of a body of mass M(≫ m). The particle is moving in a circular orbit of radius r0 with time period T0 around the mass M. Then, the particle is subjected to an additional central force, corresponding to the potential energy Vc(r) = mα/r3, where α is a positive constant of suitable dimensions and r is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius r0 in the combined gravitational potential due to M and Vc(r), but with a new time period T1, then\(\left({\mathrm{T}}_{1}^{2}-{\mathrm{T}}_{0}^{2}/{\mathrm{T}}_{1}^{2}\right)\) is given by
[G is the gravitational constant.]
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A light planet is revolving around a massive star in a circular orbit of radius \(R\) with a period of revolution \(T\). If the force of attraction between planet and star is proportional to \(R ^{-3 / 2}\) then choose the correct option :
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In hydrogen like system the ratio of coulomb force and gravitational force between an electron and a proton is in the order of :[JEE Main 2024, 5 Apr (Shift 1)]
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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : The kinetic energy needed to project a body of mass m from earth surface to infinity is \(\frac{1}{2}\mathrm{mgR}\), where R is the radius of earth.
Reason R : The maximum potential energy of a body is zero when it is projected to infinity from earth surface.
In the light of the above statements, choose the correct answer from the option given below
[JEE Main 2023, 24 Jan (Shift 1)]
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The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be:
[JEE Main 2024, 27 Jan (Shift 1)]
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The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be:
[JEE Main 2024, 27 Jan (Shift 1)]
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The acceleration due to gravity on the surface of earth is \(g\). If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :
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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun.
Reason \(( R )\) : The moon takes less time to move around the earth than the time taken by the earth to move around the sun.
In the light of the above statements, choose the most appropriate answer from the options given below :
[JEE Main 2024, 27 Jan (Shift 2)]
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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun.
Reason \(( R )\) : The moon takes less time to move around the earth than the time taken by the earth to move around the sun.
In the light of the above statements, choose the most appropriate answer from the options given below :
[JEE Main 2024, 27 Jan (Shift 2)]
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Satellite A is launched into a circular orbit of radius R. Satellite B is launched into a circular orbit of radius 1.03R. By approximately what percentage is the time period of B greater than that of A?
(Shift I - Memory Based)
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The escape velocity from the surface of the Earth is \(11.2 \mathrm{~km} / \mathrm{s}\). Find the escape velocity from a planet whose radius is 2 times that of Earth and mass is 8 times that of Earth.
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Two planet A and B are revolving around a massive star such that \(r_A=2 r_B\) and \(m_A=4 \sqrt{3} m_B\). Find ratio of angular momentum of planet B to planet A.(Shift - II Memory Based)
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The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will be,
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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion (A): Earth has atmosphere whereas moon doesn't have any atmosphere.
Reason (R): The escape velocity on moon is very small as compared to that on earth.
In the light of the above statement, choose the correct answer from the options given below :
[JEE Main 2023, 6 Apr (Shift 1)]
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Inside a uniform spherical shell :
(A) the gravitational field is zero
(B) the gravitational potential is zero
(C) the gravitational field is same everywhere
(D) the gravitational potential is same everywhere
(E) all the above
Choose the correct answer from the options given below :
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Two satellites P and Q are moving in different circular orbits around the Earth (radius R). The heights of P and Q from the Earth surface are hP and hQ, respectively, where hP = R/3. The accelerations of P and Q due to Earth’s gravity are gP and gQ, respectively. If \(\frac{{g}_{P}}{{g}_{Q}}=\frac{36}{25},\) what is the value of \({h}_{Q}\)?
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The weight of a body on the surface of the earth is \(100 N\). The gravitational force on it when taken at a height, from the surface of earth, equal to one fourth the radius of the earth is:
[JEE Main 2023, 6 Apr (Shift 2)]
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The height ' \(h\) ' at which the weight of a body will be the same as that at the same depth ' \(h\) ' from the surface of the earth is (Radius of the earth is \(R\) and effect of the rotation of the earth is neglected)
[JEE Main 2020, 2 Sep (Shift 2)]
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If \(R_E\) be the radius of Earth, then the ratio between the acceleration due to gravity at a depth ' \(r\) ' below and a height \(' r '\) above the earth surface is:
[JEE Main 2023, 10 Apr (Shift 2)]
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Given below are two statements :
Statement-I: For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases.
Statement-II: Escape velocity is independent of the radius of the planet.
In the light of above statements, choose the most appropriate answer from the options given below
[JEE Main 2023, 13 Apr (Shift 2)]
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The escape velocities of two planets \(A\) and \(B\) are in the ratio \(1: 2\). If the ratio of their radii respectively is \(1: 3\), then the ratio of acceleration due to gravity of planet \(A\) to the acceleration of gravity of planet \(B\) will be:
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A body of mass \(m\) is taken from the earth surface to a height \(h\) equal to twice the radius of earth \(\left(R_e\right)\), the increase in potential energy will be: \((g=\) acceleration due to gravity on the surface of Earth)[JEE Main 2023, 25 Jan (Shift 2)]
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The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of \(9.0 \times\) \(10^3 km\). Find the mass of Mars. (\(\text{Given }\frac{4{\pi }^{2}}{G}=6\times {10}^{11}{N}^{-1}{m}^{-2}k{g}^{2}\))
[JEE Main 2021, 27 Jul (Shift 2)]
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The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will be,
[JEE Main 2023, 29 Jan (Shift 2)]
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An object is allowed to fall from a height \(R\) above the earth, where \(R\) is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be
[JEE Main 2023, 30 Jan (Shift 2)]
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The escape velocity from the Earths surface is \( v \). The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is
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Choose the incorrect statement from the following: [JEE Main 2023, 6 Apr (Shift 2)]
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Consider a binary star system of star A and star B with masses \(m_A\) and \(m_B\), revolving in a circular orbit of radii \(r_A\) and \(r_B\), respectively. If \(T_A\) and \(T_B\) are the time period of star \(A\) and star \(B\), respectively, then:
[JEE Main 2021, 20 July (Shift 2)]
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A body is released from a height equal to the radius \((R)\) of the earth. The velocity of the body when it strikes the surface of the earth will be :
(Given \(g=\) acceleration due to gravity on the earth.)
[JEE Main 2021, 26 Feb (Shift 1)]
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A body weight \(W\), is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be:
[JEE Main 2023, 31 Jan (Shift 2)]
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A body of mass m is taken from earth surface to the height h equal to twice the radius of earth (Re), the increase in potential energy will be:
(g = acceleration due to gravity on the surface of Earth)
[JEE Main 2023, 25 Jan (Shift 2)]
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Given below are statements : One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Earth has atmosphere whereas moon doesn’t have any atmosphere.
Reason R : The escape velocity on moon is very small as compared to that on earth.
In the light of the above statements, choose the correct answer from the options given below.
[JEE Main 2023, 6 Apr (Shift 1)]
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Two planets \(A\) and \(B\) of radii \(R\) and \(1.5 R\) have densities \(\rho\) and \(\rho / 2\) respectively. The ratio of acceleration due to gravity at the surface of \(B\) to \(A\) is :
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Consider two satellites \(S_{1}\) and \(S_{2}\) with periods of revolution \(1hr\ \)and 8 hr respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite \(S_{1}\) to the angular velocity of \(S_{2}\)
[JEE Main 2021, 24 Feb (Shift 2)]
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Choose the incorrect statement from the following :
[JEE Main 2023, 6 Apr (Shift 2)]
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Suppose the law of gravitational attraction suddenly changes and becomes an inverse cube law i.e. \(\mathrm{F}\propto \frac{1}{{\mathrm{r}}^{3}}\), but still remaining a central force. Then
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A satellite is launched into a circular orbit of radius \( r \) around earth while a second satellite is launched into an orbit of radius \( 1.02 \mathrm{r} \). The percentage difference in the time period of the two satellites is
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A body of mass \(m\) is taken from the earth surface to a height \(h\) equal to twice the radius of earth \(\left(R_e\right)\), the increase in potential energy will be: \((g=\) acceleration due to gravity on the surface of Earth)
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Given below are two statements:
Statement-I: Rotation of the earth shows effect on the value of acceleration due to gravity \((g)\).
Statement-II: The effect of rotation of the earth on the value of ' \(g\) ' at the equator is minimum and that at the pole is maximum.
In the light of the above statements, choose the correct answer from the options given below.
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At a certain depth " \(d\) " below surface of earth. value of acceleration due to gravity becomes four times that of its value at a height \(3 R\) above earth surface. Where \(R\) is Radius of earth (Take \(R=6400 km\) ). The depth \(d\) is equal to;
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T is the time period of a simple pendulum on the earth's surface. Its time period becomes x T when taken to a height R (equal to earth's radius) above the surface of earth. Then, the value of x will be:
[JEE Main 2023, 25 Jan (Shift 1)]
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Given below are two statements:
Statement-I: Acceleration due to gravity is different at different places on the surface of earth.
Statement-II: Acceleration due to gravity increases as we go down below the earth's surface.
In the light of the above statements, choose the correct answer from the options given below
[JEE Main 2023, 1 Feb (Shift 1)]
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Two planets \(A\) and \(B\) of radii \(R\) and \(1.5 R\) have densities \(\rho\) and \(\rho / 2\) respectively. The ratio of acceleration due to gravity at the surface of \(B\) to \(A\) is :
[JEE Main 2023, 13 Apr (Shift 2)]
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If the angular momentum of a planet of mass \( m \), moving around the sun in a circular orbit is \( L \), about the center of the sun, its areal velocity is:
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Two satellites A and B move round the earth in the same orbit. The mass of A is twice the mass of B. The quantity which is same for the two satellites will be:[JEE Main 2023, 12 Apr (Shift 1)]
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At a certain depth "d" below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height 3R above earth surface. Where R is Radius of earth (Take R = 6400km). The depth d is equal to
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Consider two satellites \(S_{1}\) and \(S_{2}\) with periods of revolution \(1 \ hr\ \)and 8 hr respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite \(S_{1}\) to the angular velocity of \(S_{2}\).
[JEE Main 2021, 24 Feb (Shift 2)]
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If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately:
[Take \(g=10 ms ^{-2}\), the radius of earth, \(R=6400 \times 10^3 m\), Take \(\pi=3.14]\)
[JEE Main 2021, 18 Mar (Shift 2)]
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Every planet revolves around the sun in an elliptical orbit.
1. the force acting on planet is inversely proportional to square of distance from sun.
2. Force acting on planet is inversely proportional to product of the masses of the planet and the sun.
3. The Centripetal force acting on the planet is directed away from the sun.
4. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit.
Choose the most appropriate answer from the options given below:
[JEE Main 2023, 25 Jan (Shift 2)]
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A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height \(h\) is _______ s.
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Two satellites of masses \(m\) and \(3 m\) revolve around the earth in circular orbits of radii r & 3r respectively. The ratio of orbital speeds of the satellites respectively is:
[JEE Main 2023, 10 Apr (Shift 1)]
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If \(R_E\) be the radius of Earth, then the ratio between the acceleration due to gravity at a depth ' \(r\) ' below and a height \(' r '\) above the earth surface is:
[JEE Main 2021, 31 Aug (Shift 2)]
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A planet has double the mass of the earth. Its average density is equal to the that of the earth. An object weighing \(W\) on earth will weight on that planet:
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The escape velocities of two planets A and B are in the ratio 1: 2. If the ratio of their radii respectively is 1: 3, then the ratio of acceleration due to gravity of planet A to the acceleration of gravity of planet B will be:
[JEE Main 2023, 1 Feb (Shift 2)]
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If the angular momentum of a planet of mass \( m \), moving around the sun in a circular orbit is \( L \), about the center of the sun, its areal velocity is:[JEE Main 2021, 18 Mar (Shift 2)]
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The escape velocities of two planets \(A\) and \(B\) are in the ratio \(1: 2\). If the ratio of their radii respectively is \(1: 3\), then the ratio of acceleration due to gravity of planet \(A\) to the acceleration of gravity of planet \(B\) will be:[JEE Main 2023, 1 Feb (Shift 2)]
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The ratio of escape velocity of a planet to the escape velocity of earth will be:
Given : Mass of the planet is 16 times mass of earth and radius of the planet is 4 times the radius of earth.
[JEE Main 2023, 24 Jan (Shift 2)]
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Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth \(d=\frac{R}{2}\) from the surface of earth, if its weight on the surface of earth is \(200 N\), will be:
(Given R = Radius of earth) [JEE Main 2023, 10 Apr (Shift 1)]
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The mass density of a spherical galaxy varies as \( \frac{\mathrm{K}}{\mathrm{r}} \) over a large distance \( r \) from it's centre. In that region, a small star is in a circular orbit of radius \( \mathrm{R} \). Then the period of revolution, \( \mathrm{T} \) depends on \( \mathrm{R} \) as
[JEE Main 2020, 2 Sep (Shift 1)]
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A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing W on earth will weight on that planet:
[JEE Main 2023, 6 Apr (Shift 1)]
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Two particle of equal mass ‘m’ move in a circle of radius ‘r’ under the action of their mutual gravitational attraction. The speed of each particle will be:
[JEE Main 2023, 29 Jan (Shift 1)]
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The weight of a body on the earth is \(400 N\). Then weight of the body when taken to a depth half of the radius of the earth will be:[JEE Main 2023, 8 Apr (Shift 1)]
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The weight of a body on the surface of the earth is \(100 N\). The gravitational force on it when taken at a height, from the surface of earth, equal to one fourth the radius of the earth is:
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At a certain depth " \(d\) " below surface of earth. value of acceleration due to gravity becomes four times that of its value at a height \(3 R\) above earth surface. Where \(R\) is Radius of earth (Take \(R=6400 km\) ). The depth \(d\) is equal to:
[JEE Main 2023, 31 Jan (Shift 1)]
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If \({V}_{0}\) is the gravitational potential due to sphere of uniform density on it's surface, then it's value at \(r=\frac{R}{2}\) of sphere will be: (Radius of sphere = R)[JEE Main 2023, 11 Apr (Shift 2)]
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A body weight W, is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be:
[JEE Main 2023, 31 Jan (Shift 2)]
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A planet has double the mass of the earth. Its average density is equal to the that of the earth. An object weighing \(W\) on earth will weight on that planet:
[JEE Main 2019, 12 Apr (Shift 1)]
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