Question

Assertion :A man is standing at the centre on a horizontal rotating turntable (rotating on a smooth horizontal surface) has two dumbbells in his hands. If he brings them closer to himself, the kinetic energy of the whole system increases. Reason: In absence of external torque kinetic energy of system remains conserved.

• A. Assertion is True, Reason is True; Reason is a correct explanation for Assertion.
• B. Assertion is True, Reason is True; Reason is NOT a correct explanation for Assertion.
• C. Assertion is True, Reason is False.
• D. Assertion is False, Reason is True.

Answer 1

The correct option is C Assertion is True, Reason is False.

Statement-1:
As there is no external torque acting on the system ( turn table + person ), angular momentum will be conserved. As he brings both dumbells closer to himself, angular speed will increase since moment of inertia of the dumbells decreases due to decrease in r.
$K_{rot}=\frac{L^2}{2I}$
L is conserved. When I decreases, $K_{rot}$ increases.
In the absence of external torque L is conserved, not kinetic energy.