Question

A rigid body has translational as well as rotational motion. if a force couple is applied on the object then, which of the following quantities remains unchanged due to the force couple?

a. rotational K. E.
b. translation K. E
c. total K. E
d. angular moment about CM

Answer 1

The translational kinetic energy of an object remains unchanged when a force couple is applied, since a force couple only causes pure rotational effects without impacting translational motion.

Step-by-step explanation:

If a force couple is applied to an object which exhibits both translational and rotational motion, the quantity that remains unchanged is translational kinetic energy (b). A force couple consists of two equal and opposite forces acting on an object, which results in a pure rotational effect without an accompanying translational force. Therefore, while it can affect the rotational kinetic energy and angular momentum about the center of mass (CM), it does not result in a net force on the body, leaving the translational kinetic energy unchanged.

Rotational kinetic energy and angular momentum can change if a torque acts on the object, as per the work-energy theorem for rotational motion. This rotational energy is dependent on the object's moment of inertia and its angular velocity. However, since a force couple does not cause any linear acceleration or deceleration, the translational kinetic energy, which depends on the mass and the velocity of the object's center of mass, is unaffected.

Answer 2

When a force couple is applied to a rigid body, the translational kinetic energy remains unchanged, as a force couple does not result in a net external force. The correct option is D that the angular momentum about the center of mass remains unchanged.

Step-by-step explanation:

When a force couple is applied to a rigid body, it creates a torque without resulting in a net external force on the body. This means that while the force couple might change the rotational aspects of the body's motion, it will not affect its translational motion. The torque produced will not change the translational kinetic energy (K.E.), but it can alter the rotational kinetic energy and the angular momentum of the body, depending on the time it acts and the body's moment of inertia.

Given the choices provided, we can analyze each to understand the effect of a force couple:

• (a) Rotational K.E. - This can change because the force couple can accelerate or decelerate the body's rotation.
• (b) Translation K.E. - This remains unchanged because a force couple does not result in any net external force that would alter translational motion.
• (c) Total K.E. - This may change if rotational kinetic energy changes.
• (d) Angular momentum about CM - This remains unchanged assuming no external torque acts on the body, as angular momentum is conserved in the absence of external torques.

Thus, the mention correct option is (d) angular momentum about CM.