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JEE • PHYSICS • UNITS & MEASUREMENTS

Units & measurements practice · Hard

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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1 Hard

1 of 15

Analyzing +4 | -1

If velocity of light c, acceleration due to gravity g and density d are the fundamental quantities in a system of measurement then mass has

View answer and explanation

Correct option: D

dimensions 6 in c

Option D (dimensions 6 in c) is correct because dimensional analysis shows that mass is proportional to c⁶ * g^-3 * d¹.

2 Hard

2 of 15

Analyzing +4 | -1

A student performs an experiment for determination of

\mathrm{g}\left( { = \frac{{4{\mathrm{\pi }^2}l}}{{{T^2}}}} \right),\mathrm{\;}l \approx 1\mathrm{m},

, and he commits an error of

\Delta l.

. For T he takes the time of n oscillations with the stop watch of least count ∆T and he commits a human error of 0.1 s. For which of the following data, the measurement of g will be most accurate?

View answer and explanation

Correct option: D

\Delta L = 0.5,\;\Delta T = 0.05,\;n = 50

Option D (

\Delta L = 0.5, \Delta T = 0.05, n = 50

) is correct because it minimizes the percentage error in g by having a smaller error in time period measurement and a larger number of oscillations.

3 Hard

3 of 15

Application +4 | -1

In the relation

p = \frac{\mathrm{\alpha }}{\mathrm{\beta }}\mathrm{\;}{\mathrm{e}^{ - \frac{{\alpha z}}{{k\mathrm{\theta }}}}},\mathrm{\;}p

, is the pressure, z the distance, k is Boltzmann constant and

\theta

is the temperature, the dimensional formula of

\beta

will be

View answer and explanation

Correct option: A

\left[ {{\mathrm{M}^0}{\mathrm{L}^2}{\mathrm{T}^0}} \right]

Option A (

{{\mathrm{M}^0}{\mathrm{L}^2}{\mathrm{T}^0}}

) is correct because it is the dimensional formula derived by equating dimensions in the given relation.

4 Hard

4 of 15

Analyzing +4 | -1

Velocity of sound in a medium is given by

{A^{1/2}}\,{d^{ - 1/2}}

where

d

is density of medium. Then

A

represents

View answer and explanation

Correct option: A

Elastic constant

Option A (Elastic constant) is correct because the dimensional analysis of the given expression matches the dimensions of an elastic constant.

5 Hard

5 of 15

Analyzing +4 | -1

In the determination of Young’s modulus

\left( {Y = \frac{{4\;MLg}}{{\pi \;\ell {d^2}}}} \right)

by using Searle’s method, a wire of length L=2m and diameter d=0.5mm is used. For a load M=2.5 kg, an extension

\ell = 0.25mm

in the length of the wire is observed. Quantities d and

\ell

are measured using a screw gauge and a micrometer, respectively. They have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to the maximum probable scale is 100. The contributions to the maximum probable error of the Y measurement

View answer and explanation

Correct option: A

Due to the errors in the measurements of d and

\ell

are the same

Option A is correct because the percentage error in both d and l measurements is the same (2%).

6 Hard

6 of 15

Application +4 | -1

A wire has mass

(0.3\, \pm \,0.003)\,gm,

radius

(0.5 \pm \,0.005)\,cm\,

and length

(6 \pm \,0.06)\,cm\,

. The maximum percentage error in the measurement of its density is:-

View answer and explanation

Correct option: D

Option D (4%) is correct because the maximum percentage error in density is the sum of the percentage errors in mass, length, and twice the percentage error in radius.

7 Hard

7 of 15

Analyzing +4 | -1

x

is the depression produced in the middle of a beam of length

l

breadth b and thickness d and a load of mass m is attached at the centre of the beam. If y is the young Modulus of the material. Which of the following is dimensionally correct

View answer and explanation

Correct option: B

x = \frac{{mg{l^3}}}{{4\,b{d^3}y}}

Option D (

x = \frac{{mg{l^3}}}{{4\,b{d^3}y}}

) is correct because it is the only option where the dimensions of both sides of the equation match, resulting in length.

8 Hard

8 of 15

Analyzing +4 | -1

Pressure gradient has the same dimension as that of

View answer and explanation

Correct option: D

None of these

Option D (None of these) is correct because the dimension of pressure gradient is

[ML^{-2}T^{-2}]

, which does not match the dimensions of velocity gradient, potential gradient, or energy gradient.

9 Hard

9 of 15

Application +4 | -1

Velocity

\left( v \right)

and acceleration

\left( a \right)

in two systems of units 1 and 2 are related as

{v_2} = \frac{n}{{{m^2}}}{v_1}

and

{a_2} = \frac{{{a_1}}}{{mn}}

respectively. Here

m

and

n

are constants. The relations for distance and time in two systems respectively are:

View answer and explanation

Correct option: A

\frac{{{n^3}}}{{{m^3}}}{L_1} = {L_2}\,\,{\text{and}}\,\,\frac{{{n^2}}}{m}{T_1} = {T_2}

Option A (

\frac{{{n^3}}}{{{m^3}}}{L_1} = {L_2}\,\,{\text{and}}\,\,\frac{{{n^2}}}{m}{T_1} = {T_2}

) is correct because it correctly relates the distance and time units between the two systems based on the given velocity and acceleration relationships.

10 Hard

10 of 15

Analyzing +4 | -1

The mass of the liquid flowing per second per unit area of cross-section of the tube is proportional to (pressure difference across the ends)

^n

and (average velocity

^m

of the liquid. Which one of the following relation is correct?

View answer and explanation

Correct option: B

m=-n

Option B (

m=-n

) is correct because dimensional analysis shows that the exponents must be equal in magnitude but opposite in sign.

11 Hard

11 of 15

Analyzing +4 | -1

Given a charge

q,

current

I

and permeability of vacuum

\mu_0.

Which of the following quantity has the dimension of momentum?

View answer and explanation

Correct option: B

q \mu_0 I

Option B (

q \mu_0 I

) is correct because the dimensional analysis confirms that the product of charge, permeability of vacuum, and current has the dimensions of momentum.

12 Hard

12 of 15

Remembering +4 | -1

To determine refractive index of glass also using
a travelling microscope, minimum number of
readings required are

View answer and explanation

Correct option: C

Three

Option C (Three) is correct because three readings are needed: one for the real depth, one for the apparent depth with the glass slab, and one as a reference point.

13 Hard

13 of 15

Application +4 | -1

A unit of area, often used in measuring land areas, is the hectare defined as

{10^4}\,{m^2}

. An open-pit coal mine consumes 75 hectares of land, down to a depth of 26m, each year. What volume of earth, in cubic kilometre, is removed in this time?

View answer and explanation

Correct option: B

0.02

Option B (0.02) is correct because it is the result of calculating the volume of earth removed in cubic kilometers.

14 Hard

14 of 15

Application +4 | -1

A wire has mass

(0.3\, \pm \,0.003)\,gm,

radius

(0.5 \pm \,0.005)\,cm\,

and length

(6 \pm \,0.06)\,cm\,

. The maximum percentage error in the measurement of its density is:-

View answer and explanation

Correct option: D

0.04

Option D (4%) is correct because the maximum percentage error in density is the sum of the percentage errors in mass, length, and twice the percentage error in radius.

15 Hard

15 of 15

Analyzing +4 | -1

The liquid drop of density

\rho ,

radius

r

and surface tension

\sigma

oscillates with time period T. Which of the following expression for

{T^2}

is correct

View answer and explanation

Correct option: A

\frac{{\rho {r^3}}}{\sigma }

Option A (

\frac{{\rho {r^3}}}{\sigma }

) is correct because dimensional analysis confirms this relationship between the variables.

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Key Takeaways

✓ This set contains 15 single-correct-answer MCQs on UNITS & MEASUREMENTS.
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