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JEE • PHYSICS • UNITS & MEASUREMENTS

Units & measurements practice · Mixed difficulty

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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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Showing 1-30 of 616 questions
1 Easy
1 of 616
Analyzing +4 | -1
Assertion :  Modulus of elasticity  Density \sqrt{\frac{\text { Modulus of elasticity }}{\text { Density }}} has the unit ms−1. \mathrm{ms}^{-1} \text {. }

Reason: Acceleration has the dimensions of 1(ε0μ0)t. \frac{1}{\left(\sqrt{\varepsilon_0 \mu_0}\right) t} \text {. }
View answer and explanation
Correct option: B
If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
Option B (If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion) is correct because both statements are true, but the reason does not explain the assertion.
2 Medium
2 of 616
Analyzing +4 | -1
The method of dimensional analysis can be used to derive which of the following relations?
View answer and explanation
Correct option: D
None of the above
Option D (None of the above) is correct because dimensional analysis cannot be used to derive relations involving transcendental functions or sums of terms with different dimensions.
3 Easy
3 of 616
Understanding +4 | -1
Statement-I: Dimensions of constant of proportionality of constants can be derived from dimensional method
Statement-II: Numerical value of constant of proportionality can be found from experiments only
View answer and explanation
Correct option: A
Statement-I is true and statement-II is true
Option A (Statement-I is true and statement-II is true) is correct because dimensional analysis can derive the dimensions of proportionality constants, but their numerical values require experimental determination.
4 Medium
4 of 616
Remembering +4 | -1
The dimensions of torque are
View answer and explanation
Correct option: B
[ML2 T−2]\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]
Option B ([ML2 T−2]\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]) is correct because torque is force times distance, and its dimensions are mass times length squared times time to the power of -2.
5 Medium
5 of 616
Analyzing +4 | -1
The physical quantity having the dimensions [M−1L−3A2T3]\left[ {{\mathrm{M}^{ - 1}}{\mathrm{L}^{ - 3}}{\mathrm{A}^2}{T^3}} \right] is
View answer and explanation
Correct option: C
Electrical conductivity
Option C is correct. The dimensions given correspond to electrical conductivity, which is the inverse of resistivity.
6 Medium
6 of 616
Analyzing +4 | -1
A quantity X is given by ε0LΔVΔt,  {\varepsilon _0}L\frac{{\Delta V}}{{\Delta t}},\;, where ε0{\varepsilon _0} is the permittivity of free space, L is a length, ΔV{\Delta V} is a potential difference and Δt{\Delta t} is a time interval. The dimensional formula for X is the same as that of
View answer and explanation
Correct option: D
Electric current
Option D (Electric current) is correct because the given expression has the same dimensions as electric current.
7 Medium
7 of 616
Application +4 | -1
If L=2.331  cm,  B=2.1  cm,L = 2.331\;cm,\;B = 2.1\;cm, then L+B=
View answer and explanation
Correct option: C
4.4 cm
Option C (4.4 cm) is correct because the sum of L and B, considering significant figures, is 4.4 cm.
8 Medium
8 of 616
Application +4 | -1
The density of wood is 0.5 in C.G.S system of units. The corresponding value in M.K.S unit is
View answer and explanation
Correct option: A
500
Option A (500) is correct because converting the density from C.G.S to M.K.S units results in 500 kg/m³.
9 Medium
9 of 616
Analyzing +4 | -1
Assertion: The equation y=2x+ty=2 x+t is physically incorrect if x & yx \,\&\, y are distances and tt is time.
Reason: Quantities with different dimensions cannot be added or subtracted.
View answer and explanation
Correct option: A
If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion
Option A is correct because the equation is dimensionally incorrect, and quantities with different dimensions cannot be added.
10 Easy
10 of 616
Analyzing +4 | -1
Assertion : The number of significant figures depends on the least count of measuring instrument.

Reason : Significant figures define the accuracy of measuring instrument.
View answer and explanation
Correct option: B
If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
Option B (If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion) is correct because both statements are true, but the reason doesn't directly explain the assertion.
11 Medium
11 of 616
Analyzing +4 | -1
Given equation 12mv2=mgh\frac{1}{2} m v^2=m g h, where mm is the mass of the body, vv is velocity, gg is the acceleration due to gravity and hh is the height. Then the given equation is
View answer and explanation
Correct option: B
Dimensionally correct
Option B (Dimensionally correct) is correct because both sides of the equation have the same dimensions (ML2T−2ML^2T^{-2}).
12 Hard
12 of 616
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.
13 Medium
13 of 616
Understanding +4 | -1
Which of the following quantities is dimensionless
View answer and explanation
Correct option: D
None
Option D (None) is correct because Gravitational constant, Planck's constant, and Power of a convex lens all have dimensions.
14 Easy
14 of 616
Application +4 | -1
The surface tension of mercury is 32 dyne cm−1\mathrm{c}{\mathrm{m}^{ - 1}}. Its value in SI units is
View answer and explanation
Correct option: A
0.032
Option A (0.032) is correct because the surface tension in SI units is obtained by converting dyne/cm to N/m, resulting in 0.032 N/m.
15 Medium
15 of 616
Understanding +4 | -1
The dimensions of electric potential are
View answer and explanation
Correct option: A
[ML2T−2Q−1]\left[ {\mathrm{M}{\mathrm{L}^2}{\mathrm{T}^{ - 2}}{\mathrm{Q}^{ - 1}}} \right]
Option A (ML2T−2Q−1{\mathrm{M}{\mathrm{L}^2}{\mathrm{T}^{ - 2}}{\mathrm{Q}^{ - 1}}}) is correct because it represents the dimensions of energy per unit charge, which is the definition of electric potential.

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16 Medium
16 of 616
Analyzing +4 | -1
Of the following quantities, which one has the dimensions different from the remaining three?
View answer and explanation
Correct option: D
Angular momentum per unit mass
Option D (Angular momentum per unit mass) is correct because it has different dimensions compared to energy density, force per unit area, and the product of charge per unit volume and voltage.
17 Medium
17 of 616
Understanding +4 | -1
Which of the following is most precise measurement?
View answer and explanation
Correct option: D
0.0005 m0.0005 \mathrm{~m}
Option D (0.0005 m) is correct because the smaller the least count of a measuring instrument, the more precise the measurement.
18 Medium
18 of 616
Analyzing +4 | -1
The physical quantity which is not a unit of energy is
View answer and explanation
Correct option: B
MeV-sec
Option B (MeV-sec) is correct because it represents energy multiplied by time, not energy itself.
19 Medium
19 of 616
Understanding +4 | -1
Dimensions of bulk modulus are
View answer and explanation
Correct option: B
[ML−1T−2]\left[ {\mathrm{M}{\mathrm{L}^{ - 1}}{\mathrm{T}^{ - 2}}} \right]
Option B [ML−1T−2]\left[ {\mathrm{M}{\mathrm{L}^{ - 1}}{\mathrm{T}^{ - 2}}} \right] is correct because it represents the dimensions of bulk modulus, which is stress divided by strain.
20 Medium
20 of 616
Understanding +4 | -1
In the equation y=asin⁡(ωt+kx)y=a \sin (\omega t+k x), the dimensional formula of ω\omega is
View answer and explanation
Correct option: A
[M0 L0 T−1]\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^{-1}\right]
Option A ([M⁰ L⁰ T⁻¹]) is correct because the argument of the sine function must be dimensionless, so ωt has dimensions of 1, making ω have dimensions of T⁻¹.
21 Easy
21 of 616
Remembering +4 | -1
Candela is the unit of
View answer and explanation
Correct option: B
Luminous intensity
Option B (Luminous intensity) is correct because candela is the SI unit of luminous intensity, which measures the amount of light emitted by a source in a particular direction.
22 Medium
22 of 616
Application +4 | -1
The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5 % and 1 %, the maximum error in determining the density is
View answer and explanation
Correct option: C
0.045
Option C (4.50%) is correct because it is the maximum error calculated using the formula for density and the given relative errors.
23 Easy
23 of 616
Understanding +4 | -1
Which of the following statement(s) is/are incorrect?
View answer and explanation
Correct option: C
Absolute error cannot be negative.
Option Absolute error cannot be negative. is correct because absolute error can be positive or negative, while systematic and random errors are different types of errors, and absolute error is the difference between real and measured values.
24 Medium
24 of 616
Understanding +4 | -1
Which of the following numerical values has three significant figures?
View answer and explanation
Correct option: D
0.3000.300
Option D (0.3000.300) is correct because trailing zeros after the decimal point are significant, giving it three significant figures.
25 Easy
25 of 616
Remembering +4 | -1
Light year is a unit of
View answer and explanation
Correct option: C
Distance
Option C (Distance) is correct because a light-year is defined as the distance light travels in one year, making it a unit of distance.
26 Medium
26 of 616
Analyzing +4 | -1
Given that υ is speed, r is the radius and g is the acceleration due to gravity. Which of the following is dimensionless
View answer and explanation
Correct option: A
υ2/rg{\upsilon ^2}/rg
Option A (υ2/rg{\upsilon ^2}/rg) is correct because the expression is dimensionless, as it represents the square of speed divided by the product of radius and acceleration due to gravity, resulting in a dimensionless quantity.
27 Easy
27 of 616
Understanding +4 | -1
Which of the following statement(s) is/are incorrect?
View answer and explanation
Correct option: C
Both light year and wavelength represent time.
Option C is correct because both light year and wavelength have dimensions of length, not time.
28 Medium
28 of 616
Application +4 | -1
If P represents radiations pressure, c represents speed of light and Q represents radiation energy striking a unit area per second, the non-zero integers x,y and z such that PxQycz{P^x}{Q^y}{c^z} is dimensionless, are
View answer and explanation
Correct option: B
x=1,  y=−1,  z=1x = 1,\;y = - 1,\;z = 1
Option B (x=1,  y=−1,  z=1x = 1,\;y = - 1,\;z = 1) is correct because it satisfies the dimensional analysis equation, making the expression dimensionless.
29 Medium
29 of 616
Analyzing +4 | -1
Velocity of object is given as a function of time and position.
v=αt+βx+γv=\alpha t+\beta x+\gamma

then dimension of α,β\alpha, \beta and γ\gamma are
View answer and explanation
Correct option: B
LT−2,T−1,LT−1L T^{-2}, T^{-1}, L T^{-1}
Option B (LT−2,T−1,LT−1L T^{-2}, T^{-1}, L T^{-1}) is correct because it correctly derives the dimensions of alpha, beta, and gamma by equating the dimensions of each term in the equation.
30 Medium
30 of 616
Remembering +4 | -1
The unit of Stefan's constant σ\sigma is:
View answer and explanation
Correct option: C
Wm−2K−4W m^{-2} K^{-4}
Option C (Wm−2K−4W m^{-2} K^{-4}) is correct because Stefan's constant relates the power radiated per unit area of a black body to the fourth power of its absolute temperature, and its unit is derived from the Stefan-Boltzmann law.
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