Laws of Motion

A car of \(800 kg\) is taking turn on a banked road of radius \(300 m\) and angle of banking \(30^{\circ}\). If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely : \(\left( g =10 m / s ^2, \sqrt{3}=1.73\right)\)

[JEE Main 2024, 06 Apr (Shift 2)]

A massless spring gets elongated by amount \({x}_{1}\) under a tension of 5 N . Its elongation is \({x}_{2}\) under the tension of 7 N . For the elongation of \(\left(5{x}_{1}-2{x}_{2}\right)\), the tension in the spring will be,

[JEE Main 2025, 23 Jan (Shift 2)]

A massless spring gets elongated by amount \({x}_{1}\) under a tension of 5 N . Its elongation is \({x}_{2}\) under the tension of 7 N . For the elongation of \(\left(5{x}_{1}-2{x}_{2}\right)\), the tension in the spring will be,

[JEE Main 2025, 23 Jan (Shift 2)]

A cricket player catches a ball of mass \(120 g\) moving with \(25 m / s\) speed. If the catching process is completed in \(0.1 s\) then the magnitude of force exerted by the ball on the hand of player will be (in SI unit):EndFragment

[JEE Main 2024, 01 Feb (Shift 2)]

A cricket player catches a ball of mass \(120 g\) moving with \(25 m / s\) speed. If the catching process is completed in \(0.1 s\) then the magnitude of force exerted by the ball on the hand of player will be (in SI unit):EndFragment

[JEE Main 2024, 01 Feb (Shift 2)]

A massless spring gets elongated by amount \({x}_{1}\) under a tension of 5 N . Its elongation is \({x}_{2}\) under the tension of 7 N . For the elongation of \(\left(5{x}_{1}-2{x}_{2}\right)\), the tension in the spring will be:

An artillery piece of mass \(M_1\) fires a shell of mass \(M_2\) horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is:

[JEE Main 2024, 31 Jan (Shift 1)]

An artillery piece of mass \(M_1\) fires a shell of mass \(M_2\) horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is:

[JEE Main 2024, 31 Jan (Shift 1)]

At \(t=0\), a body of mass 100 g starts moving under the influence of a force \((5\hat{i}+10\hat{j})N\). After 2s its position is \((2x\hat{i}+5y\hat{j})m\). The ratio x: y is ___________ .

[JEE Main 2026, 4 Apr (Shift 2)]

An object with mass \(500g\) moves along x -axis with speed \(v=4\sqrt{x}\mathrm{m}/\mathrm{s}\). The force acting on the object is :

[JEE Main 2025, 7 Apr (Shift 2)]

A balloon of mass M is ascending with an acceleration a. What fraction of its mass should be dropped so that it starts moving upward with an acceleration of 3 a ?

(Shift - II Memory Based)

A balloon of mass M is ascending with an acceleration a. What fraction of its mass should be dropped so that it starts moving upward with an acceleration of 3 a ?

(Shift - II Memory Based)

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): An electric fan continues to rotate for some time after the current is switched off.
Reason (R): Fan continues to rotate due to inertia of motion.
In the light of above statements, choose the most appropriate answer from the options given below.
[JEE Main 2023, 10 Apr (Shift 2)]

A bullet of mass \(10\mathrm{g}\) leaves the barrel of gun with a velocity of \(600\mathrm{m}/\mathrm{s}\). If the barrel of the gun is \(50\mathrm{cm}\) long and mass of gun is \(3\mathrm{kg}\), then value of impulse supplied to the gun will be:

[JEE Main 2023, 13 Apr (Shift 1)]

100 balls each of mass \(m\) moving with speed v simultaneously strike a wall normally and are reflected back with the same speed, in time t s. The total force exerted by the balls on the wall is

A bullet of ' \(4 g\) ' mass is fired from a gun of mass \(4 kg\). If the bullet moves with the muzzle speed of \(50 ms ^{-1}\), the impulse imparted to the gun velocity of recoil of gun are:

[JEE Main 2021, 22 Jul (Shift 2)]

A machine gun of mass \(10\mathrm{kg}\) fires \(20\mathrm{g}\) bullets at the rate of 180 bullets per minute with a speed of\(100{\mathrm{ms}}^{-1}\) each. The recoil velocity of the gun is:

[JEE Main 2023, 30 Jan (Shift 2)]

An average force of \(125 \mathrm{~N}\) is applied on a machine gun firing bullets each of mass \(10 \mathrm{~g}\) at the speed of \(250 \mathrm{~m} / \mathrm{s}\) to keep it in position. The number of bullets fired per second by the machine gun is :

[JEE Main 2023, 11 Apr (Shift 1)]

A particle of mass \(M\) originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation

\(\mathrm{F}=\mathrm{F}_0\left(1-\left(\frac{\mathrm{t}-\mathrm{T}}{\mathrm{T}}\right)^2\right)\)

Where \(F_0\) and \(T\) are constants. The force acts only for the time internal \(2 T\). The velocity \(v\) of the particle after time \(2 T\) is -

[JEE Main 2021, 27 Jul (Shift 2)]

A bullet of mass \(10\mathrm{g}\) leaves the barrel of gun with a velocity of \(600\mathrm{m}/\mathrm{s}\). If the barrel of the gun is \(50\mathrm{cm}\) long and mass of gun is \(3\mathrm{kg}\), then value of impulse supplied to the gun will be:

At any instant, the velocity of a particle of mass \(500\mathrm{g}\) is \(\left(2t\hat{i}+3{t}^{2}\hat{j}\right){\mathrm{ms}}^{-1}\). If the force acting on the particle at \(t=1\mathrm{s}\) is \((\hat{i}+x\hat{j})N\). Then the value of x will be:

[JEE Main 2023, 8 Apr (Shift 1)]

A machine gun of mass \(10\mathrm{kg}\) fires \(20\mathrm{g}\) bullets at the rate of 180 bullets per minute with a speed of\(100{\mathrm{ms}}^{-1}\) each. The recoil velocity of the gun is:

A force \(\vec{F}=(40\hat{i}+10\hat{j})N\) acts on a body of mass \(5\mathrm{kg}\). If the body starts from rest, its position vector \(\vec{r}\) at time \(t=10\mathrm{s}\), will be:

[JEE Main 2021, 25 Jul (Shift 2)]

100 balls each of mass \(m\) moving with speed v simultaneously strike a wall normally and are reflected back with the same speed, in time t s. The total force exerted by the balls on the wall is

[JEE Main 2023, 31 Jan (Shift 1)]

A block of mass \(5 kg\) is placed at rest on a table of rough surface. Now, if a force of \(30 N\) is applied in the direction parallel to surface of the table, the block slides through a distance of \(50 m\) in an interval of time \(10 s\). Coefficient of kinetic friction is (given, \(g=10 ms ^{-2}\) ):

[JEE Main 2023, 1 Feb (Shift 1)]

A particle of mass \(M\) originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation

\(\mathrm{F}=\mathrm{F}_0\left(1-\left(\frac{\mathrm{t}-\mathrm{T}}{\mathrm{T}}\right)^2\right)\)

Where \(F_0\) and \(T\) are constants. The force acts only for the time internal \(2 T\). The velocity \(v\) of the particle after time \(2 T\) is -

The time taken by an object to slide down a \(45^{\circ}\) rough inclined plane is \(n\) times as it takes to slide down a perfectly smooth \(45^{\circ}\) inclined plane. The coefficient of kinetic friction between the object and the incline plane is

[JEE Main 2024, 08 Apr (Shift 2)]

A particle of mass m is moving in the x y-plane such that its velocity at a point (x, y) is given as \(\vec{v}=\alpha (y\hat{x}+2x\hat{y})\), where \(\alpha\) is a non-zero constant. What is the force \(\vec{F}\) acting on the particle?

[JEE Advanced 2023]

An average force of 125 N is applied on a machine gun firing bullets each of mass 10g at the speed of 250 m/s to keep it in position. The number of bullets fired per second by the machine gun is :

[JEE Main 2023, 11 Apr (Shift 1)]

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): An electric fan continues to rotate for some time after the current is switched off.
Reason (R): Fan continues to rotate due to inertia of motion.
In the light of above statements, choose the most appropriate answer from the options given below.

A body of mass \(500 \mathrm{~g}\) moves along \(\mathrm{x}\)-axis such that it's velocity varies with displacement \(x\) according to the relation \(v=10 \sqrt{x} \mathrm{~m} / \mathrm{s}\) the force acting on the body is:-

[JEE Main 2023, 11 Apr (Shift 2)]