Units and Measurements

32 JEE Main questions · Physics

Significant figures & errors

PhysicsJEE Main 21 Jan 2026, Shift 1·Q5·MCQ·Easy–moderate
Open
In an experiment the values of two spring constants were measured as $k_1 = (10 \pm 0.2)$ N/m and $k_2 = (20 \pm 0.3)$ N/m. If these springs are connected in parallel, then the percentage error in equivalent spring constant is:
1. (1)2.67%
2. (2)2.33%
3. (3)1.33%
4. (4)1.67%
PhysicsJEE Main 21 Jan 2026, Shift 2·Q11·MCQ·Easy
Open
Keeping the significant figures in view, the sum of the physical quantities 52.01m, 153.2 m and 0.123 m is :
1. (1)205 m
2. (2)205.333 m
3. (3)205.33 m
4. (4)205.3 m
PhysicsJEE Main 21 Jan 2026, Shift 2·Q12·MCQ·Easy–moderate
Open
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 associated with $\sigma$ , $\rho$ and g, gravitational acceleration)
1. (1) $2\dfrac{\Delta r}{r} - \dfrac{\Delta v_0}{v_0}$
2. (2) $\dfrac{2\Delta r}{r} + \dfrac{\Delta v_0}{v_0}$
3. (3) $2\left[\dfrac{\Delta r}{r} + \dfrac{\Delta v_0}{v_0}\right]$
4. (4) $2\left[\dfrac{\Delta r}{r} - \dfrac{\Delta v_0}{v_0}\right]$
PhysicsJEE Main 23 Jan 2026, Shift 1·Q4·MCQ·Easy–moderate
Open
Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm and 18.25 cm. The relative error in the measurement of average length of the rod is:
1. (1)0.24
2. (2)0.18
3. (3)0.06
4. (4)0.08
PhysicsJEE Main 23 Jan 2026, Shift 1·Q19·MCQ·Easy–moderate
Open
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 the circular scale reading is 51 then the correct thickness of the sheet is mm.
[Assume least count is 0.01 mm]
1. (1)1.50
2. (2)1.48
3. (3)1.54
4. (4)1.51
PhysicsJEE Main 23 Jan 2026, Shift 2·Q10·MCQ·Easy–moderate
Open
To compare EMF of two cells using potentiometer the balancing lengths obtained are 200 cm and 150 cm. The least count of scale is 1 cm. The percentage error in the ratio of EMFs is
1. (1)1.45
2. (2)1.65
3. (3)1.75
4. (4)1.55
Flawed question. No option is correct: $(1/200 + 1/150)\times100 = 1.17\%$ (the source's own solution says no option matches) and no evident intended version gives the key 1.65. It is shown for completeness and is left out of practice tests.
PhysicsJEE Main 24 Jan 2026, Shift 2·Q2·MCQ·Easy–moderate
Open
In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division $= 0.05$ mm, then the least count of the vernier callipers is mm.
1. (1)0.002
2. (2)0.05
3. (3)0.02
4. (4)0.005
PhysicsJEE Main 28 Jan 2026, Shift 1·Q17·MCQ·Easy–moderate
Open
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 of a cylinder, observer observes 15 divisions on main scale and $5^{\text{th}}$ division of vernier scale coincides with a main scale division. Measured length of cylinder is mm. (Least count of Vernier calliper $= 0.1$ mm)
1. (1)15.4
2. (2)15.1
3. (3)15.5
4. (4)15.9
We corrected a printing error in the original paper
Source printed “coincides with a min scale division”.
PhysicsJEE Main 28 Jan 2026, Shift 2·Q7·MCQ·Easy
Open
In an experiment, a set of readings are obtained 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.
1. (1)0.01
2. (2)0.001
3. (3)0.1
4. (4)0.05
We corrected a printing error in the original paper
Source printed “a set of reading are obtained $-1.24$ mm” (stray minus sign on the first reading).
PhysicsJEE Main 28 Jan 2026, Shift 2·Q19·MCQ·Easy–moderate
Open
The time period of a simple harmonic oscillator is $T = 2\pi\sqrt{\dfrac{m}{k}}$ . The 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 s resolution. Percentage error in determination of spring constant( $k$ ) is %.
1. (1)3.43
2. (2)3.35
3. (3)7.60
4. (4)6.76
We corrected a printing error in the original paper
Source printed “ $T = 2\pi\sqrt{k/m}$ ” ( $k$ and $m$ interchanged).
PhysicsJEE Main 2 Apr 2026, Shift 1·Q2·MCQ·Moderate
Open
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 by a micrometer of least count 0.001 cm. The error in the measured Young's modulus is $\alpha\times10^{9}\ \mathrm{N/m^2}$ . The value of $\alpha$ is .
(Ignore the contribution of the load to Young's modulus error calculation)
1. (1)1.3
2. (2)1.65
3. (3)0.13
4. (4)0.25
PhysicsJEE Main 2 Apr 2026, Shift 2·Q7·MCQ·Easy–moderate
Open
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 sphere is measured, the reading of main scale is 5 mm and $50^{\text{th}}$ division of circular scale coincides with the reference line of main scale. The diameter of sphere is mm.
1. (1)5.045
2. (2)5.055
3. (3)5.450
4. (4)5.550
PhysicsJEE Main 4 Apr 2026, Shift 1·Q1·MCQ·Easy–moderate
Open
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.
1. (1) $1\times10^{-2}$
2. (2) $1\times10^{-3}$
3. (3) $5\times10^{-2}$
4. (4) $5\times10^{-3}$
PhysicsJEE Main 5 Apr 2026, Shift 1·Q1·MCQ·Easy–moderate
Open
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 division is 1 mm and there are 10 Vernier scale divisions, then the Vernier caliper has
1. (1)0.07 cm negative zero error
2. (2)0.7 cm negative zero error
3. (3)0.07 cm positive zero error
4. (4)0.7 cm positive zero error
PhysicsJEE Main 5 Apr 2026, Shift 2·Q2·MCQ·Easy–moderate
Open
In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as 10V and 5 A, respectively. The least counts of voltmeter and ammeter are 500 mV and 200 mA, respectively. The estimated error in the resistance measurement is $\Omega$
1. (1)0.25
2. (2)2
3. (3)2.5
4. (4)0.18
PhysicsJEE Main 6 Apr 2026, Shift 1·Q1·MCQ·Easy–moderate
Open
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 $97.42 \pm 0.02$ g, $8.35 \pm 0.05$ mm and $20.20 \pm 0.02$ mm, respectively. Calculated percentage fractional error in $\rho$ is .
1. (1)0.63%
2. (2)0.82%
3. (3)0.72%
4. (4)0.25%
PhysicsJEE Main 6 Apr 2026, Shift 2·Q1·MCQ·Easy–moderate
Open
The percentage error in the calculated volume of a sphere, if there is 2% error in its diameter measurement, is .
1. (1)1
2. (2)2
3. (3)6
4. (4)8

Dimensional analysis

PhysicsJEE Main 21 Jan 2026, Shift 1·Q7·MCQ·Easy–moderate
Open
Consider a modified Bernoulli equation. $\left(P + \frac{A}{Bt^2}\right) + \rho g(h + Bt) + \frac12\rho V^2 = \text{constant}$ If $t$ has the dimension of time then the dimensions of $A$ and $B$ are , respectively.
1. (1) $[\mathrm{ML^0T^{-1}}]$ and $[\mathrm{M^0LT}]$
2. (2) $[\mathrm{ML^0T^{-1}}]$ and $[\mathrm{M^0LT^{-1}}]$
3. (3) $[\mathrm{ML^0T^{-2}}]$ and $[\mathrm{M^0LT^{-2}}]$
4. (4) $[\mathrm{ML^0T^{-2}}]$ and $[\mathrm{M^0LT^{-1}}]$

PhysicsJEE Main 22 Jan 2026, Shift 1·Q19·MCQ·Easy–moderate

Match the LIST-I with LIST-II

	List-I		List-II
A.	Spring constant	I.	$\mathrm{ML^2T^{-2}K^{-1}}$
B.	Thermal conductivity	II.	$\mathrm{ML^0T^{-2}}$
C.	Boltzmann constant	III.	$\mathrm{ML^2T^{-3}A^{-2}}$
D.	Inductive reactance	IV.	$\mathrm{MLT^{-3}K^{-1}}$

Choose the correct answer from the options given below:

(1)(A)-(II), (B)-(I), (C)-(IV), (D)-(III)
(2)(A)-(I), (B)-(IV), (C)-(II), (D)-(III)
(3)(A)-(III), (B)-(II), (C)-(IV), (D)-(I)
(4)(A)-(II), (B)-(IV), (C)-(I), (D)-(III)

PhysicsJEE Main 22 Jan 2026, Shift 2·Q1·MCQ·Easy–moderate
Open
If $\epsilon$ , E and t represent the free space permittivity, electric field and time respectively, then the unit of $\dfrac{\epsilon E}{t}$ will be :
1. (1)Am
2. (2) $\mathrm{Am^2}$
3. (3) $\mathrm{A/m^2}$
4. (4)A/m
PhysicsJEE Main 23 Jan 2026, Shift 2·Q23·Numerical·Easy–moderate
Open
A ball of radius $r$ and density $\rho$ dropped through a viscous liquid of density $\sigma$ and viscosity $\eta$ attains its terminal velocity at time $t$ , given by $t = A\,\rho^{a}\,r^{b}\,\eta^{c}\,\sigma^{d}$ , where $A$ is a constant and $a$ , $b$ $c$ and $d$ are integers. The value of $\dfrac{b+c}{a+d}$ is .

PhysicsJEE Main 24 Jan 2026, Shift 1·Q1·MCQ·Easy–moderate

Open

Match the List-I with List-II

List-I		List-II
A.	Magnetic induction	I.	$\mathrm{M\,L\,T^{-2}A^{-2}}$
B.	Magnetic flux	II.	$\mathrm{M\,L^{2}\,T^{-2}A^{-2}}$
C.	Magnetic permeability	III.	$\mathrm{M\,L^{0}\,T^{-2}A^{-1}}$
D.	Self inductance	IV.	$\mathrm{M\,L^{2}\,T^{-2}A^{-1}}$

Choose the correct answer from the options given below:

(1)(A)-(IV), (B)-(III), (C)-(I), (D)-(II)
(2)(A)-(III), (B)-(IV), (C)-(II), (D)-(I)
(3)(A)-(I), (B)-(III), (C)-(IV), (D)-(II)
(4)(A)-(III), (B)-(IV), (C)-(I), (D)-(II)

PhysicsJEE Main 28 Jan 2026, Shift 2·Q20·MCQ·Easy

Open

Match List-I with List-II.

	List-I		List-II
A.	Coefficient of viscosity	I.	$[\mathrm{ML^{-1}T^{-2}}]$
B.	Surface tension	II.	$[\mathrm{ML^{2}T^{-2}}]$
C.	Pressure	III.	$[\mathrm{ML^{0}T^{-2}}]$
D.	Surface energy	IV.	$[\mathrm{ML^{-1}T^{-1}}]$

Choose the correct answer from the options given below:

(1)(A)-(I), (B)-(II), (C)-(IV), (D)-(III)
(2)(A)-(IV), (B)-(III), (C)-(I), (D)-(II)
(3)(A)-(I), (B)-(III), (C)-(II), (D)-(IV)
(4)(A)-(IV), (B)-(I), (C)-(II), (D)-(III)

PhysicsJEE Main 2 Apr 2026, Shift 1·Q1·MCQ·Easy–moderate
Open
The dimensional formula of $\dfrac12\epsilon_0E^2$ ( $\epsilon_0 =$ permittivity of vacuum and $E =$ electric field) is $\mathrm{M^aL^bT^c}$ . The value of $2a - b + c =$ .
1. (1)0
2. (2)1
3. (3) $-1$
4. (4)2
PhysicsJEE Main 2 Apr 2026, Shift 2·Q1·MCQ·Easy–moderate
Open
Dimensions of universal gravitational constant (G) in terms of Planck's constant ( $h$ ), distance ( $L$ ), mass ( $M$ ) and time ( $T$ ) are .
1. (1) $[\mathrm{hTLM^{-2}}]$
2. (2) $[\mathrm{hT^{-1}LM^{-2}}]$
3. (3) $[\mathrm{hTL^{2}M^{-2}}]$
4. (4) $[\mathrm{h^{-1}T^{-1}LM^{-2}}]$

PhysicsJEE Main 4 Apr 2026, Shift 2·Q1·MCQ·Easy

Open

Match the LIST-I with LIST-II

List-I		List-II
A.	Planck's constant	I.	$\mathrm{ML^2T^{-2}}$
B.	Stopping potential	II.	$\mathrm{T^{-1}}$
C.	Work function	III.	$\mathrm{ML^2T^{-1}}$
D.	Threshold frequency	IV.	$\mathrm{ML^2T^{-3}A^{-1}}$

Choose the correct answer from the options given below:

(1)(A)-(III), (B)-(IV), (C)-(I), (D)-(II)
(2)(A)-(I), (B)-(II), (C)-(III), (D)-(IV)
(3)(A)-(IV), (B)-(III), (C)-(I), (D)-(II)
(4)(A)-(I), (B)-(IV), (C)-(III), (D)-(II)

PhysicsJEE Main 5 Apr 2026, Shift 1·Q2·MCQ·Easy–moderate
Open
L, C and R represent physical quantities inductance, capacitance and resistance respectively. The dimensional formula $\mathrm{M\,L^{2}T^{-4}A^{-2}}$ corresponds to .
1. (1) $\dfrac{R}{\sqrt{LC}}$
2. (2) $\dfrac{R}{LC}$
3. (3) $\dfrac{C}{\sqrt{LR}}$
4. (4) $\dfrac{1}{R}\sqrt{\dfrac{L}{C}}$
We corrected a printing error in the original paper
Source printed “represents”.

PhysicsJEE Main 5 Apr 2026, Shift 2·Q1·MCQ·Easy–moderate

Open

Match List-I with List-II.

List-I	List-II
(A) Meter (L)	I. $\sqrt{\dfrac{hc}{\mathrm{G}}}$
[6pt] (B) Second (S)	II. $\sqrt{\dfrac{\mathrm{G}h}{\mathrm{c}^5}}$
[6pt] (C) Kilogram (M)	III. $\sqrt{\dfrac{\mathrm{K^2L^2c^3}}{\mathrm{G}h}}$
[6pt] (D) Kelvin (K)	IV. $\sqrt{\dfrac{\mathrm{G}h}{\mathrm{c}^3}}$

where h (Planck's constant), G (gravitational constant) and c (speed of light in vacuum) are taken as fundamental units.

Choose the correct answer from the options given below:

(1)A-II, B-IV, C-I, D-III
(2)A-IV, B-II, C-I, D-III
(3)A-IV, B-I, C-II, D-III
(4)A-III, B-I, C-II, D-IV

We corrected a printing error in the original paper

Source printed “c (speed of light in vacuum) as fundamental units” (verb missing).

PhysicsJEE Main 6 Apr 2026, Shift 1·Q2·MCQ·Easy–moderate
Open
The potential energy of a particle changes with distance x from a fixed origin as $V = \dfrac{A\sqrt{x}}{x + B}$ , where A and B are constants with appropriate dimensions. The dimensions of AB are .
1. (1) $[\mathrm{M^1L^{5/2}T^{-2}}]$
2. (2) $[\mathrm{M^{3/2}L^{5/2}T^{-2}}]$
3. (3) $[\mathrm{M^1L^2T^{-2}}]$
4. (4) $[\mathrm{M^1L^{7/2}T^{-2}}]$
We corrected a printing error in the original paper
Source printed “A and B are constant with appropriate dimensions. The dimension of AB are”.

PhysicsJEE Main 6 Apr 2026, Shift 2·Q2·MCQ·Easy–moderate

Open

Match List-I with List-II.

	List-I		List-II
A.	Boltzmann constant	I.	$[\mathrm{M^{-1}L^{3}T^{-2}}]$
B.	Stefan's constant	II.	$[\mathrm{M\,L^{2}T^{-1}}]$
C.	Planck's constant	III.	$[\mathrm{ML^{2}T^{-2}K^{-1}}]$
D.	Gravitational constant	IV.	$[\mathrm{ML^{0}T^{-3}K^{-4}}]$

(1)(A)-(I), (B)-(II), (C)-(III), (D)-(IV)
(2)(A)-(IV), (B)-(III), (C)-(II), (D)-(I)
(3)(A)-(III), (B)-(IV), (C)-(II), (D)-(I)
(4)(A)-(II), (B)-(I), (C)-(IV), (D)-(III)

PhysicsJEE Main 8 Apr 2026, Shift 2·Q2·MCQ·Moderate
Open
Consider the equation $H = \dfrac{x^{p}\,\epsilon^{q}\,E^{r}}{t^{s}}$
Where $H =$ magnetic field intensity; $E =$ electric field; $\epsilon =$ permittivity, $x =$ distance, $t =$ time. The values of $p$ , $q$ , $r$ and $s$ respectively are:
1. (1)1, 1, 1, 1
2. (2) $-1$ , 1, 2, 1
3. (3)1, $-1$ , $-2$ , 1
4. (4) $-1$ , $-2$ , $-2$ , 1
We corrected a printing error in the original paper
Source printed “ $H =$ magnetic field” (with $H = B$ in tesla no option fits); corrected to the intended “ $H =$ magnetic field intensity” (A/m).

Units and SI

PhysicsJEE Main 8 Apr 2026, Shift 2·Q1·MCQ·Easy
Open
A new unit ( $\alpha$ ) of length is chosen such that it is equal to the distance travelled by light in vacuum in 1 s. What is the distance between Venus and Earth in terms of $\alpha$ units if light takes 6 min. 40 s to cover this distance?
1. (1) $200\,\alpha$
2. (2) $400\,\alpha$
3. (3) $300\,\alpha$
4. (4) $500\,\alpha$
We corrected a printing error in the original paper
Source printed “such that it is equal to the speed of light in vacuum” (a length cannot equal a speed); corrected to the intended “equal to the distance travelled by light in vacuum in 1 s”.