Units and Measurements

Consider the diameter of-a spherical object being measured with the help of a Vernier callipers. Suppose its \(10\) Vernier Scale Divisions (V.S.D.) are equal to its 9 Main Scale Divisions (M.S.D.). The least division in the M.S. is \(0.1\) cm and the zero of V.S. is at \(x=0.1\mathrm{cm}\) when the jaws,of Vernier callipers are closed. If the main scale reading for the diameter is \(\mathrm{M}=5\mathrm{cm}\) and the number of coinciding vernier division is \(8\) , the measured diameter after zero error correction, is

In an electrical circuit, the voltage is measured as \(V=(200\pm 4)\) volt and the current is measured as \(\mathrm{I}=(20\pm 0.2)\mathrm{A}\). The value of the resistance is;

[Re-NEET 2024]

The potential energy of a particle moving along \(X\)-direction varies as \(V=\frac{A{x}^{2}}{\sqrt{x}+B}\). where x is distance, The dimensions of \(\frac{{A}^{2}}{B}\) are:

A force defined by \(F=\alpha {t}^{2}+\beta t\) acts on a particle at a given time t. The factor which is dimensionless, if \(\alpha\) and \(\beta\) are constants, is:

[NEET 2024]

A physical quantity P is related to four observations a, b, c and d as follows: \(\mathrm{P}={\mathrm{a}}^{3}{\mathrm{b}}^{2}/\mathrm{c}\sqrt{\mathrm{d}}\). The percentage errors of measurement in a, b, c and d are \(1\%,3\%,2\%\), and \(4\%\) respectively. The percentage error in the quantity P is

[NEET 2025]

The pitch of an error free screw gauge is \(1\mathrm{mm}\) and there are 100 divisions on the circular scale. While measuring the diameter of a thick wire, the pitch scale reads \(1\mathrm{mm}\) and \({63}^{\text{rd }}\) division on the circular scale coincides with the reference line. The diameter of the wire is:

In a vernier callipers, 20 VSD coincide with 16 MSD (each division of length 1 mm ). The least count of the vernier callipers is :

In a vernier calipers, (N+1) divisions of vernier scale coincide with N divisions of main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is :

The pitch of an error free screw gauge is \(1\mathrm{mm}\) and there are 100 divisions on the circular scale. While measuring the diameter of a thick wire, the pitch scale reads \(1\mathrm{mm}\) and \({63}^{\text{rd }}\) division on the circular scale coincides with the reference line. The diameter of the wire is:

The quantities which have the same dimensions as those of solid angle are :

[NEET 2024]

In a vernier calipers, (N+1) divisions of vernier scale coincide with N divisions of main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is :

In an electrical circuit, the voltage is measured as \(V=(200\pm 4)\) volt and the current is measured as \(\mathrm{I}=(20\pm 0.2)\mathrm{A}\). The value of the resistance is;

Each side of a metallic cube of mass 5.580 kg is measured to be 9.0 cm. Keeping the significant figures in view, the density of the material of the cube can be best expressed as X × 10³ kg m⁻³, where the value of X is:

A huge circular arc of length 4.4 ly subtends an angle ' \(4 s\) ' at the centre of the circle. How long it would take for a body to complete 4 revolution if its speed is \(8 AU\) per second?
Given : \(1 ly =9.46 \times 10^{15} m\)

[JEE Main 2021, 27 Aug (Shift 1)]

The pitch of the screw gauge is \(1\mathrm{mm}\) and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies 8 divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while \({72}^{\text{nd }}\)division on circular scale coincides with the reference line, The radius of the wire is:

[JEE Main 2021, 25 Feb (Shift 1)]

Young's modulus of elasticity Y is expressed in terms of three derived quantities, namely, the gravitational constant G. Planck's constant h and the speed of light c, as \(Y={c}^{\alpha }{h}^{\beta }{G}^{\gamma }\). Which of the following is the correct option ?

[JEE Advanced 2023]

A quantity \( f \) is given by \( f=\sqrt{\frac{h c^{5}}{G}} \), where \( c \) is speed of light, \( G \) universal gravitational constant and \( h \) is the Planck’s constant. Dimension of \( f \) is that of

[JEE Main 2020, 9 Jan (Shift 1)]

Electric field in a certain region is given by \(\vec{E}=\left(\frac{A}{{x}^{2}}\hat{i}+\frac{B}{{y}^{3}}\hat{j}\right)\). The SI unit of A and B are:

[JEE Main 2023, 30 Jan (Shift 1)]

Dimensions of stress are

If time (\(\mathrm{t})\), velocity (\(\nu)\), and angular momentum (\(\mathrm{l})\) are taken as the fundamental units. Then the dimension of mass (\(\mathrm{m})\) in terms of \(\mathrm{t}\), \(\boldsymbol{\nu}\) and \(\mathrm{l}\) is:

[JEE Main 2021, 20 Jul (Shift 2)]

\(\left(P+\frac{a}{{V}^{2}}\right)(V-b)=RT\) represents the equation of state of some gases. Where P is the pressure, V is the volume, T is the temperature and a, b, R are the constants. The physical quantity, which has dimensional formula as that of \(\frac{{b}^{2}}{a}\), will be:

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

The period of oscillation of a simple pendulum is \(T=2\pi \sqrt{\frac{L}{g}}\). Measured value of ' L ' is \(1.0\mathrm{m}\) from meter scale having a minimum division of \(1\mathrm{mm}\) and time of one- complete oscillation is \(1.95\mathrm{s}\) measured from stopwatch of \(0.01\mathrm{s}\) resolution. The percentage error in the determination of ' g ' will be:

If E, L, M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula \(P=E{L}^{2}{M}^{-5}{G}^{-2}\) are :-

[JEE Main 2021, 26 Aug (Shift 1)]

A screw gauge gives the following readings when used to measure the diameter of a wire
Main scale reading : 0 mm
Circular scale reading : 52 divisions
Given that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is:
[NEET 2021]

If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity \(\frac{1}{4\pi {\epsilon }_{0}}\frac{|e{|}^{2}}{hc}\) has dimensions of:

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

Two resistors \({R}_{1}=(4\pm 0.8)\Omega\) and \({R}_{2}=(4\pm 0.4)\Omega\) are connected in parallel. The equivalent resistance of their parallel combination will be:

[JEE Main 2021, 1 Sep (Shift 2)]

Dimensions of stress are

[NEET 2020]

Match List-I with List-II:

Choose the correct answer from the options given below:

[JEE Main 2021, 25 Feb (Shift 1)]

Dimensions of \( 1 /\left(\mu_{0} \varepsilon_{0}\right) \) is:

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

The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are :

[NEET 2023]

A screw gauge has least count of \( 0.01 \mathrm{~mm} \) and there are \( 50 \) divisions in its circular scale.The pitch of the screw gauge is:

[NEET 2020]

A body of mass \((5\pm 0.5)\mathrm{kg}\) is moving with a velocity of \((20\pm 0.4)\mathrm{m}/\mathrm{s}\). Its kinetic energy will be

If \(E\) and \(G\) respectively denote energy and gravitational constant, then \(\frac{E}{G}\) has the dimensions of:

[NEET 2021]

A cylindrical wire of mass \((0.4\pm 0.01)g\) has length \((8\pm 0.04)\mathrm{cm}\) and radius \((6\pm 0.03)\mathrm{mm}\). The maximum error in its density will be:

A metal wire has mass \((0.4\pm 0.002)\mathrm{g}\), radius \(\left(0.3\pm 0.001\right)\)mm and length \((5\pm 0.02)\mathrm{cm}\). The maximum possible percentage error in the measurement of density will nearly be :

[NEET 2023]

The intervals measured by a clock given the following readings: \( 1.25 \mathrm{~s}, 1.24 \mathrm{~s}, 1.27 \mathrm{~s}, 1.21 \mathrm{~s} \) and \( 1.28 \mathrm{~s} \). What is the percentage relative error is the observations?

If force \( (\mathrm{F}) \), velocity (V) and time \( (\mathrm{T}) \) are taken as fundamental units, then the dimensions of mass are

[NEET 2021]

Consider the following statements about vernier calipers:

Statement I: In a vernier calipers, one vernier scale division is smaller than one main scale division.

Statement II: The vernier constant is given by one main scale division multiplied by the number of vernier

Taking into account of the significant figures, what is the value of \( 9.99 \mathrm{~m}-0.0099 \mathrm{~m} \) ?