A mass m moves in a circle on a smooth horizontal plane with...

A mass $\text{m}$ moves in a circle on a smooth horizontal plane with velocity ${v}_{0}$ at a radius ${R}_{0}$ . The mass is attached to a string which passes through a smooth hole in plane as shown.

A mass m moves in a circle on a smooth horizontal plane with velocity v _ 0 at a radius R _ 0 . The mass is attached to

The tension in the string is increased gradually and finally $\text{m}$ moves in a circle of radius $\dfrac{{R}_{0}}{2}$ . The final value of the kinetic energy is:

Options

A $m{v}_{0}^{2}$
B $\dfrac{1}{4}m{v}_{0}^{2}$
C $2m{v}_{0}^{2}$
D $\dfrac{1}{2}m{v}_{0}^{2}$

Correct answer

C. $2m{v}_{0}^{2}$

Step-by-step solution

From conservation of angular momentum.

\begin{aligned} & m v_0 R_0=m v^{\prime}\left(\frac{R_0}{2}\right) \\ & \Rightarrow v^{\prime}=2 v_0 \end{aligned}

) Hence, final (K E=\frac{1}{2} m v^{\prime 2}=\frac{1}{2} m\left(2 v_0\right)^2) Final

KE=2 m v_0^2

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