Free Dimensional Analysis MCQs with Answers

1. The second equation of motion of a uniformly accelerated ball along a straight line is stated ass = vft +1/2 at2The dimension of this equation is

• A. [L]
• B. [T]
• C. [L][T-1]
• D. [L][T-2]

Explanation: The second equation of motion is s = vft + 1/2 at2. The dimension of the first term vft is [L][T-1][T] = [L]. The dimension of the second term 1/2 at2 is [L][T-2][T2] = [L]. Since both terms have the same dimensions, the overall dimension of the equation is [L]. Option D is therefore the correct answer. Options A, B, and C are incorrect as they do not represent the dimensional analysis of the entire equation.

2. Which of the following shows the dimensions of force and acceleration respectively?

• A. MLT-2 and LT-2
• B. ML2 T and LT-2
• C. MLT-2 and LT2
• D. MLT-2 and LT-1

Explanation: Force (F) is defined by Newton's second law as mass (m) multiplied by acceleration (a) (F = ma).* The dimension of mass is [M] (Mass).* The dimension of acceleration is [L][T]^-2 (Length per time squared).Therefore, the dimension of Force is [M][L][T]^-2.Dimensions of Acceleration:Acceleration (a) is the rate of change of velocity, which is velocity per unit time. Velocity is defined as displacement per unit time.* The dimension of displacement (length) is [L].* The dimension of time is [T].* So, the dimension of velocity is [L][T]^-1.* Therefore, the dimension of acceleration is [L][T]^-1 / [T] = [L][T]^-2.

3. The second equation of motion of a uniformly accelerated ball along a straight line is stated asS=vit+ ½ at2The dimension of each term of this equation is

• A. [L]
• B. [T]
• C. [L-1]
• D. [T-1]

Explanation: The second equation of motion is given by S = vit + ½ at2, where S is the displacement, vi is the initial velocity, a is the acceleration, and t is the time. The dimension of displacement (S) is length [L]. Both terms vit and ½ at2 in the equation must also have the dimension of length to ensure dimensional consistency. Therefore, the correct dimension for S is [L]. The other options are incorrect because they do not correspond to the dimension of displacement.

4. The dimensions of momentum are represented as

• A. [MLT-1]
• B. [ML2T-1]
• C. [MLT-2]
• D. [ML-1T]

Explanation: Momentum is defined as the product of mass and velocity, so its dimensions are given by multiplying the dimensions of mass (M) and velocity (LT-1). Therefore, the dimension of momentum is [MLT-1]. Option A correctly represents these dimensions. Option B [ML2T-1] could refer to a different physical concept like angular momentum, Option C [MLT-2] represents force, and Option D [ML-1T] does not correspond to a recognized physical quantity.