Units & Measurements PYQs - Last 5 Years
JEE Main / Physics / Mechanics / 137 recent questions
PhysicsMechanics2022-2026
Practice 137 JEE Main Physics questions from Units & Measurements. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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Last 5 Years Units & Measurements Questions
Showing 50 of 137 filtered questions.
1Units And Measurements
Consider the equation $H=\frac{x^p \epsilon^q E^r}{t^s}$
Where $H=$ magnetic field; $E=$ electric field, $\epsilon=$ permittivity, $x=$ distance, $t=$ time The values of $p, q, r$ and $s$ respectively are :
Where $H=$ magnetic field; $E=$ electric field, $\epsilon=$ permittivity, $x=$ distance, $t=$ time The values of $p, q, r$ and $s$ respectively are :
MCQ+4 / -12026
2Units And Measurements
A new unit ( $\alpha$ ) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of $\alpha$ units if light takes 6 min. 40 s to cover this distance?
MCQ+4 / -12026
3Units And Measurements
The density $\rho$ of a uniform cylinder is determined by measuring its mass $m$, length $l$ and diameter $d$. The measured values of $m, l$ and $d$ are $97.42 \pm 0.02 \mathrm{~g}$, $8.35 \pm 0.05 \mathrm{~mm}$ and $20.20 \pm 0.02 \mathrm{...
MCQ+4 / -12026
4Units And Measurements
The potential energy of a particle changes with distance $x$ from a fixed origin as $V=\frac{A \sqrt{x}}{x+B}$, where $A$ and $B$ are constant with appropriate dimensions. The dimensions of $A B$ are $\_\_\_\_$
MCQ+4 / -12026
5Units And Measurements
\(\text { Match List - I with List - II. }\)
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MCQ+4 / -12026
6Units And Measurements
The percentage error in the calculated volume of a sphere, if there is $2 \%$ error in its diameter measurement, is $\_\_\_\_$ .
MCQ+4 / -12026
7Units And Measurements
$L, C$ and $R$ represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula $\mathrm{ML}^2 \mathrm{~T}^{-4} \mathrm{~A}^{-2}$ corresponds to $\_\_\_\_$ .
MCQ+4 / -12026
8Units And Measurements
In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and $7^{\text {th }}$ Vernier division coincides with a main scale reading. If the value of 1 main scale div...
MCQ+4 / -12026
9Units And Measurements
\(\text { Match List - I with List - II. }\)
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MCQ+4 / -12026
10Units And Measurements
In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as 10 V and 5 A , respectively. The least counts of voltmeter and ammeter are 500 mV and 200 mA , respectively. The e...
MCQ+4 / -12026
11Units And Measurements
In a screw gauge when the circular scale is given five complete rotations it moves linearly by 2.5 mm . If the circular scale has 100 divisions, the least count of screw gauge is $\_\_\_\_$ mm.
MCQ+4 / -12026
12Units And Measurements
\(\text { Match the LIST-I with LIST-II }\)
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MCQ+4 / -12026
13Units And Measurements
The diameter of a wire measured by a screw gauge of least count 0.001 cm is 0.08 cm. The length measured by a scale of least count 0.1 cm is 150 cm. When a weight of 100 N is applied to the wire, the extension in length is 0.5 cm, measured ...
MCQ+4 / -12026
14Units And Measurements
The dimensional formula of $\frac{1}{2} \epsilon_0 E^2$ ($\epsilon_0$ = permittivity of vacuum and $E$ = electric field) is $M^a L^b T^c$.The value of $2a - b + c =$ ________.
MCQ+4 / -12026
15Units And Measurements
In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are 100 divisions in circular scale and pitch of screw gauge is 0.1 mm. When diameter of a s...
MCQ+4 / -12026
16Units And Measurements
Dimensions of universal gravitational constant ($G$) in terms of Planck's constant ($h$), distance ($L$), mass ($M$) and time ($T$) are _______.
MCQ+4 / -12026
17Units And Measurements
When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, $4{ }^{\text {th }}$ mark on vernier scale coincides with certain mark on the main scale. While measuring the length o...
MCQ+4 / -12026
18Units And Measurements
In an experiment, a set of reading are obtained as follows - 1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm. The expected least count of the instrument used in recording these readings is _______ mm.
MCQ+4 / -12026
19Units And Measurements
Match List - I with List - II.
List – I
List – II
A. Coefficient of viscosity
B. Surface tension
C. Pressure
D. Surface energy
I. [ML−1T−2]
II. [ML2T−2]
III. [...
List – I
List – II
A. Coefficient of viscosity
B. Surface tension
C. Pressure
D. Surface energy
I. [ML−1T−2]
II. [ML2T−2]
III. [...
MCQ+4 / -12026
20Units And Measurements
The speed of a longitudinal wave in a metallic bar is 400 m/s. If the density and Young's modulus of the bar material are increased by 0.5% and 1%, respectively then the speed of the wave is changed approximately to ______ m/s.
MCQ+4 / -12026
21Units And Measurements
The time period of a simple harmonic oscillator is $T = 2\pi \sqrt{\frac{k}{m}}$. Measured value of mass $(m)$ of the object is 10 g with an accuracy of 10 mg and time for 50 oscillations of the spring is found to be 60 s using a watch of 2...
MCQ+4 / -12026
22Units And Measurements
In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division $=0.05 \mathrm{~mm}$, then the least count of the vernier callipers is $\_\_\_\_$ mm.
MCQ+4 / -12026
23Units And Measurements
Four persons measure the length of a rod as $20.00 \mathrm{~cm}, 19.75 \mathrm{~cm}, 17.01 \mathrm{~cm}$ and 18.25 cm . The relative error in the measurement of average length of the rod is :
MCQ+4 / -12026
24Units And Measurements
In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is 1 mm and t...
MCQ+4 / -12026
25Units And Measurements
\(\text { Match the LIST-I with LIST-II }\)
List-I
List-II
A.
Spring constant
I.
M
L
2
T
−
2
K
−
1
...
List-I
List-II
A.
Spring constant
I.
M
L
2
T
−
2
K
−
1
...
MCQ+4 / -12026
26Units And Measurements
If $\epsilon, E$ and $t$ represent the free space permittivity, electric field and time respectively, then the unit of $\frac{\epsilon E}{t}$ will be :
MCQ+4 / -12026
27Units And Measurements
In an experiment the values of two spring constants were measured as $k_1=(10 \pm 0.2) \mathrm{N} / \mathrm{m}$ and $k_2=(20 \pm 0.3) \mathrm{N} / \mathrm{m}$. If these springs are connected in parallel, then the percentage error in equival...
MCQ+4 / -12026
28Units And Measurements
Consider a modified Bernoulli equation.
\(\left(\mathrm{P}+\frac{A}{B t^2}\right)+\rho g(h+B t)+\frac{1}{2} \rho V^2=\text { constant }\)
If $t$ has the dimension of time then the dimensions of $A$ and $B$ are $\_\_\_\_$ , $\_\_\_\_$ resp...
\(\left(\mathrm{P}+\frac{A}{B t^2}\right)+\rho g(h+B t)+\frac{1}{2} \rho V^2=\text { constant }\)
If $t$ has the dimension of time then the dimensions of $A$ and $B$ are $\_\_\_\_$ , $\_\_\_\_$ resp...
MCQ+4 / -12026
29Units And Measurements
Keeping the significant figures in view, the sum of the physical quantities 52.01 m, 153.2 m and 0.123 m is :
MCQ+4 / -12026
30Units And Measurements
A spherical body of radius $r$ and density $\sigma$ falls freely through a viscous liquid having density $\rho$ and viscosity $\eta$ and attains a terminal velocity $v_0$. Estimated maximum error in the quantity $\eta$ is : (Ignore errors a...
MCQ+4 / -12026
31Units And Measurements
A quantity Q is formulated as $X^{-2}Y^{+\frac{3}{2}}Z^{-\frac{2}{5}}$. X, Y, and Z are independent parameters which have fractional errors of 0.1, 0.2, and 0.5, respectively in measurement. The maximum fractional error of Q is
MCQ+4 / -12025
32Units And Measurements
Match List - I with List - II.
List - I
List - II
(A) Mass density
(I) [ML2T−3]
(B) Impulse
(II) [MLT−1]
(C) Power
(III) [ML2T0]
(D) Moment of inertia
(IV) [ML−3T0]
C...
List - I
List - II
(A) Mass density
(I) [ML2T−3]
(B) Impulse
(II) [MLT−1]
(C) Power
(III) [ML2T0]
(D) Moment of inertia
(IV) [ML−3T0]
C...
MCQ+4 / -12025
33Units And Measurements
The dimension of $ \sqrt{\frac{\mu_0}{\epsilon_0}} $ is equal to that of:
($ \mu_0 $ = Vacuum permeability and $ \epsilon_0 $ = Vacuum permittivity)
($ \mu_0 $ = Vacuum permeability and $ \epsilon_0 $ = Vacuum permittivity)
MCQ+4 / -12025
34Units And Measurements
In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $M^P L^Q T^R A^S$, where value of ' $Q$ ' and ' $R$ ' are
MCQ+4 / -12025
35Units And Measurements
For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains 300 equal divisions equals to 15 cm . The vernier scale attached to the microscope has 25 divisions equals to 24 divisions of...
MCQ+4 / -12025
36Units And Measurements
In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of $\left[\mathrm{M}^{\mathrm{P}} \mathrm{L}^{\mathrm{Q}} \mathrm{T}^R A^{\mathrm{S}}\right]$. The value of P a...
MCQ+4 / -12025
37Units And Measurements
A person measures mass of 3 different particles as $435.42 \mathrm{~g}, 226.3 \mathrm{~g}$ and 0.125 g . According to the rules for arithmetic operations with significant figures, the addition of the masses of 3 particles will be.
MCQ+4 / -12025
38Units And Measurements
\(\text { Match the LIST-I with LIST-II }\)
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MCQ+4 / -12025
39Units And Measurements
A physical quantity C is related to four other quantities $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s as follows
\(C=\frac{p q^2}{r^3 \sqrt{s}}\)
The percentage errors in the measurement of $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s are $1...
\(C=\frac{p q^2}{r^3 \sqrt{s}}\)
The percentage errors in the measurement of $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s are $1...
INTEGER+4 / -12025
40Units And Measurements
Match List I with List II.
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MCQ+4 / -12025
41Units And Measurements
Given a charge q , current I and permeability of vacuum $\mu_{\mathrm{o}^*}$. Which of the following quantity has the dimension of momentum ?
MCQ+4 / -12025
42Units And Measurements
If $\mu_0$ and $\epsilon_0$ are the permeability and permittivity of free space, respectively, then the dimension of $\left(\frac{1}{\mu_0 \epsilon_0}\right)$ is :
MCQ+4 / -12025
43Units And Measurements
The expression given below shows the variation of velocity (v) with time (t),
$v=\mathrm{At}^2+\frac{\mathrm{Bt}}{\mathrm{C}+\mathrm{t}}$.
The dimension of ABC is :
$v=\mathrm{At}^2+\frac{\mathrm{Bt}}{\mathrm{C}+\mathrm{t}}$.
The dimension of ABC is :
MCQ+4 / -12025
44Units And Measurements
The pair of physical quantities not having the same dimensions is :
MCQ+4 / -12025
45Units And Measurements
$\text { A physical quantity } Q \text { is related to four observables } a, b, c, d \text { as follows : }$
$Q = \frac{ab^4}{cd}$
where, $\mathrm{a}=(60 \pm 3) \mathrm{Pa} ; \mathrm{b}=(20 \pm 0.1) \mathrm{m} ; \mathrm{c}=(40 \pm 0.2) \mat...
$Q = \frac{ab^4}{cd}$
where, $\mathrm{a}=(60 \pm 3) \mathrm{Pa} ; \mathrm{b}=(20 \pm 0.1) \mathrm{m} ; \mathrm{c}=(40 \pm 0.2) \mat...
INTEGER+4 / -12025
46Units And Measurements
Match List - I with List - II.
List - I
List - II
(A) Young’s Modulus
(I) M L-1 T-1
(B) Torque
(II) M L-1 T-2
(C) Coefficient of Viscosity
(III) M-1 L3 T-2
(D) Gravitational Co...
List - I
List - II
(A) Young’s Modulus
(I) M L-1 T-1
(B) Torque
(II) M L-1 T-2
(C) Coefficient of Viscosity
(III) M-1 L3 T-2
(D) Gravitational Co...
MCQ+4 / -12025
47Units And Measurements
A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm , respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the shee...
INTEGER+4 / -12025
48Units And Measurements
Match List - I with List - II.
List - I
List - II
(A) Angular Impulse
(I) M0 L2 T-2
(B) Latent Heat
(II) M L2 T-3 A-1
(C) Electrical resistivity
(III) M L2 T-1
(D) Electromotive...
List - I
List - II
(A) Angular Impulse
(I) M0 L2 T-2
(B) Latent Heat
(II) M L2 T-3 A-1
(C) Electrical resistivity
(III) M L2 T-1
(D) Electromotive...
MCQ+4 / -12025
49Units And Measurements
The least count of a screw guage is 0.01 mm . If the pitch is increased by $75 \%$ and number of divisions on the circular scale is reduced by $50 \%$, the new least count will be ________ $\times 10^{-3} \mathrm{~mm}$
INTEGER+4 / -12025
50Units And Measurements
For an experimental expression $y=\frac{32.3 \times 1125}{27.4}$, where all the digits are significant. Then to report the value of $y$ we should write
MCQ+4 / -12025