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Question

(C) Since the tension force acts towards the center of the circle,the torque about the center is zero. Therefore,the angular momentum of the mass $m$

Vedclass · Accepted Answer

$2mv_0^2$

Vedclass · Answer

(C) Since the tension force acts towards the center of the circle,the torque about the center is zero. Therefore,the angular momentum of the mass $m$ is conserved.Initial angular momentum $L_i = m v_0 R_0$.Final angular momentum $L_f = m v R$,where $R = \frac{R_0}{2}$.By conservation of angular momentum,$L_i = L_f$:$m v_0 R_0 = m v \left( \frac{R_0}{2} \right)$$v = 2 v_0$.The initial kinetic energy is $K_i = \frac{1}{2} m v_0^2$.The final kinetic energy is $K_f = \frac{1}{2} m v^2 = \frac{1}{2} m (2 v_0)^2 = \frac{1}{2} m (4 v_0^2) = 2 m v_0^2$.

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