Question

The analogy between linear motion and rotational motion are given. The FALSE one is:

• A. Force : Torque
• B. Linear Displacement : Angular displacement
• C. Mass : Moment of inertia
• D. Linear momentum : Angular momentum
• E. Translational energy : Vibrational energy

Hint:

The key difference in the analogy lies in the distinction between translational and vibrational motion. Translational motion involves linear displacement, while vibrational motion involves oscillations around a fixed point.

Answer 1

Answer: (E)

In physics, the analogy between linear motion and rotational motion is made by comparing various quantities. Let's analyze each option:
(A) Force : Torque
- Force in linear motion is analogous to torque in rotational motion. Both are the quantities that cause motion (linear and rotational, respectively).
(B) Linear Displacement : Angular displacement
- Linear displacement corresponds to angular displacement. In linear motion, displacement is the change in position, while in rotational motion, angular displacement refers to the angle through which a body rotates.
(C) Mass : Moment of inertia
- Mass in linear motion is analogous to moment of inertia in rotational motion. Both represent the resistance to motion—mass resists linear acceleration, while the moment of inertia resists angular acceleration.
(D) Linear momentum : Angular momentum
- Linear momentum is analogous to angular momentum. Linear momentum is the product of mass and velocity, while angular momentum is the product of moment of inertia and angular velocity.
(E) Translational energy : Vibrational energy
- This is the false analogy. Translational energy is associated with the motion of an object in a straight line, while vibrational energy refers to the energy due to the oscillation or vibration of atoms or molecules in a substance. These two are not directly analogous in the context of motion.
Thus, the correct answer is option (E), Translational energy : Vibrational energy.