Question

Which pair have not equal dimensions:

• A. Energy and torque
• B. Force and impulse
• C. Angular momentum and Plank's constant
• D. Elastic modulus and pressure

Answer 1

The Correct Option is B

To determine which pair does not have equal dimensions, we need to analyze the dimensional formulae for each of the given pairs. Let's break down each option:

1. Energy and Torque:
   • Energy is given by the formula: E = \text{Force} \times \text{Distance}
   • Therefore, the dimensional formula for energy is [M L^2 T^{-2}].
   • Torque is given by: \tau = \text{Force} \times \text{Perpendicular distance}
   • Therefore, torque also has the dimensional formula [M L^2 T^{-2}].
   • Both have the same dimensions.
2. Force and Impulse:
   • Force is defined by Newton's second law: F = m \times a, where a is acceleration.
   • The dimensional formula for force is [M L T^{-2}].
   • Impulse is the product of force and time: J = F \times t
   • The dimensional formula for impulse is [M L T^{-1}].
   • They have different dimensions.
3. Angular Momentum and Planck's Constant:
   • Angular momentum is given by: L = mvr
   • The dimensional formula for angular momentum is [M L^2 T^{-1}].
   • Planck's constant also has the same dimensions: [M L^2 T^{-1}].
   • Both have the same dimensions.
4. Elastic Modulus and Pressure:
   • Both are defined as force per unit area.
   • The dimensional formula for elastic modulus (or Young's modulus) and pressure is [M L^{-1} T^{-2}].
   • Both have the same dimensions.

Therefore, the correct answer is that Force and Impulse do not have equal dimensions.