WBJEE 2025 Units and Measurement Practice Questions with Solutions

WBJEE 2025 Units and Measurement Practice Questions with Solutions: Units and Measurement chapter covers concepts of measurements, dimensions, errors in measurements, etc. Even though the chapter is not usually considered challenging, it does feature important fundamental concepts of physics and the measurement of time, space, and distance. Every year, 1-2 questions from Units and Measurement worth one mark or two marks are asked in the WBJEE Physics paper (Paper II). If you are appearing for the WBJEE 2025 exam this year, you should go through the WBJEE 2025 Units and Measurement practice questions provided on this page to ace your preparation. As part of the WBJEE 2025 Physics syllabus PDF, Unit and Measurements covers a significant weightage. Therefore, it is essential to solve WBJEE Units and Measurements sample questions for the upcoming exam. In this article, we have provided a list of commonly asked WBJEE 2025 Units and Measurement practice questions with solutions so that you know what to expect in the examination. 

Also Check - WBJEE 2025 Physics Topic-Wise Weightage & List of Important Topics

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List of WBJEE 2025 Units and Measurement Topics for Exam Preparation

 The preparation strategy for Units and Measurement includes covering all these topics along with practice questions related to the topic. Find the detailed sub-topics for the Units and Measurements chapter in the following table. 

Although Units and Measurement is a less important topic in the WBJEE 2025 syllabus PDF featuring only 1 to 2 questions, you can still score sure shot 2-4 marks from this chapter alone. Knowing the marks weightage for a chapter helps in understanding how many questions are expected to be asked in the actual examination. In the following table, check out the detailed WBJEE 2025 Units and Measurement expected marks weightage. 

WBJEE 2025 Units and Measurement Practice Questions with Solutions

The WBJEE 2025 preparation plan includes solving the practice questions, worked out examples and formula-based applications. Let’s have a look at some of the important WBJEE 2025 Units and Measurement practice questions with solutions below. 

Q1. In an experiment, the length of an object is measured to be 6.50 cm. This measured value can be written as 0.0650 m. The number of significant figures on 0.0650 m is:

a. 3

b. 4

c. 2

d. 5

Ans. a. 3

Solution: 

Measurement of the object = 6.50cm

Number of significant figures = 3 

Now, when the measured value is converted from one unit to another unit, then the number of significant figures remains the same in both cases.

The number of significant figures in 0.0650 m is 3.

Q2. Which of the following quantities has the dimension of length? (h is Planck's constant, m is the mass of the electron and c is the velocity of light)

a. hc/m

b. h/mc2

c. h2/mc2

d. h/mc

Ans. d. h/mc

Solution: 

To determine which quantity has the dimension of length, we need to analyze the dimensions of each option provided. We have:

h as Planck's constant

m as the mass of the electron

c as the velocity of light

First, we need to recall the dimensions of these constants:

Planck's constant (h) has the dimension of action, which is energy multiplied by time:

[h] = [E].[T]

Where [E] is the dimension of energy and [T] is the dimension of time.

The dimension of energy (E) is given by [E] = [M][L]²/[T]², where [M] is mass, [L] is length, and [T] is time.

- The dimension of mass (m) is simply [M].

- The dimension of the velocity of light () is [c] = [L]/[T].

We can calculate the dimensions for each option:

Option A:

hc/m

Substituting the known dimensions:

[hc/m] = [E][T][L]/[T]/[M] = [M][L]²/[T]²[L]/[T]/[M] = [L]³

Option B:

[h/cm²] = [E] [T]/[M] [L]²/[T]² = [M][L]²/[T]²[T]/[M][L]²/[T]² = [T] = [1/c]^-1 [L]

Option C:

[h²/mc²] = ([E][T])²/[M][L]²/[T]² = [M]²[L]⁴/[T]⁴[T]²/[M][L]²/[T]² = [M][L]²

Option D:

[h/mc] = [E][T]/[M][L][T] = [M][L]²/[T]²[T]/[M][L]/[T] = [L]

Thus, the quantity that has the dimension of length is Option D. 

Q3. The Entropy (S) of a black hole can be written as S = ????kBA, where kB is the Boltzmann constant and A is the area of the black hole. The ???? has a dimension of:

a. L2

b. ML2L-1

c. L-2

d. Dimensionless

Ans. c. L^-2

Solution:

Given, S = ????kBA

where, the dimensional formula of S = [M^-1L²T^-2K^-1]

Dimensional formula of kB = [M^-1 L² T^-2 K^-1]

Dimensional formula of A = [L²]

Thus, [M^-1L²T^-2K^-1] = ????[M^-1 L² T^-2 K^-1][L²]

???? = [L^-2]

Q4. The correct dimensional formula for impulse is given by

a. ML2T-2

b. MLT-1

c. ML2t-1

d. MLT-1

Ans. b. MLT-1

Solution: 

As we know, 

Impulse, I = force (F) x  small time interval

I = ma x t [F = ma]

I = [M] [LT^-2] x [T] 

I = [MLT^-1]

Hence, the correct dimensional formula for impulse is given by [MLT^-1].

Q5. The dimension of the universal constant of gravitation, G is:

a. [ML²T^-1]

b. [M^-1L³T^-2]

c. [M^-1L²T^-2]

d. [ML³T^-2]

Ans. b. [M^-1L³T^-2]

Solution: 

The dimensions of universal constant G, is obtained by Newton's law of gravitation

F = (Gm₁m₂)/r^₂

G = (Fxr^₂)/m₁m₂

F = Force

r = Distance

m₁ and m₂ are masses

G = [M¹L³T^-2][L²]/[M][M]

= [M¹L³T^-2]/[M²] = [M^-1L³T^-2]

Q6. The density of the material of a cube can be estimated by measuring its mass and the length of one of its sides. If the maximum error in the measurement of mass and length are 0.3% and 0.2% respectively, the maximum error in the estimation of the density of the cube is approximately:

a. 1.1%

b. 0.5%

c. 0.9%

d. 0.7%

Ans. c. 0.9%

Q7. The frequency v of the radiation emitted by an atom when an electron jumps from one orbit to another is given by v = kδE, where k is a constant and δE is the change in energy level due to the transition. Then, the dimension of k is:

a. [ML²T^-2]

b. The same dimension of angular momentum

c. [ML²T^-1]

d. [M^-1L^-2T]

Ans. d. [M^-1L^-2T]

Q8. From dimensional analysis, the Rydberg constant can be expressed in terms of electric charge (e), mass (m) and Planck constant (h) as 
[Consider 1/4πε0 = 1 unit]

a. h²/me²

b. me⁴/h²

c. m²e⁴/h²

d. me²/h²

Ans. d. me2/h2

Q9. The velocity of a particle (v) at an instant t is given by v = at + bt² the dimension of b is:

a. L

b. LT^-1

c. LT^-2

d. LT^-3

Ans. d. LT-3

Q10. The Power radiated from an accelerated charged particle is given by P ∝ (pa)m/cn where q is the charge, a is the acceleration of the particle and c is the speed of light in a vacuum. From dimensional analysis, the values of  and respectively, are: 

a. m = 2, n = 2

b. m = 2, n = 3

c. m = 3, n = 2

d. M = 0, n = 1

Ans. b. m = 2, n = 3

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