Question

The pair of quantities having same dimensions is

• A. Impulse and Surface Tension
• B. Angular momentum and Work
• C. Work and Torque
• D. Young's modulus and Energy

Answer 1

The Correct Option is C

To determine which pair of quantities have the same dimensions, we need to analyze the dimensions of each quantity listed in the options.

1. Impulse (J):
   • Impulse is defined as the change in momentum.
   • Dimensional formula: [M L T^{-1}]
2. Surface Tension (T):
   • Surface tension is force per unit length.
   • Dimensional formula: [M T^{-2}]
3. Angular Momentum (L):
   • Angular momentum is defined as the moment of momentum.
   • Dimensional formula: [M L^2 T^{-1}]
4. Work (W):
   • Work is defined as force multiplied by the distance in the direction of force.
   • Dimensional formula: [M L^2 T^{-2}]
5. Torque (τ):
   • Torque is defined as the moment of force.
   • Dimensional formula: [M L^2 T^{-2}]
6. Young's Modulus (E):
   • Young's modulus is stress per strain.
   • Dimensional formula: [M L^{-1} T^{-2}]
7. Energy (E):
   • Energy has the same dimensions as work.
   • Dimensional formula: [M L^2 T^{-2}]

Now, let's compare the dimensions:

• Impulse and Surface Tension: [M L T^{-1}] and [M T^{-2}] are different.
• Angular momentum and Work: [M L^2 T^{-1}] and [M L^2 T^{-2}] are different.
• Work and Torque: [M L^2 T^{-2}] and [M L^2 T^{-2}] are the same.
• Young's modulus and Energy: [M L^{-1} T^{-2}] and [M L^2 T^{-2}] are different.

Therefore, the correct answer is Work and Torque because they have the same dimensional formula: [M L^2 T^{-2}].