Question

A mass m moves in a circle on a smooth horizontal plane with velocity v° and a radius R° . The mass is attached to a string which passes through a smooth hole in in the plane. The tension in the string is increased gradually and finally m moves in a circle of radius R°/2 . the final value of the kinetic energy is ...??

Answer 1

Answer:

The final value of Kinetic Energy is $2mv_0^2$

Explanation:

The figure is attached.

If the velocity in the circle of R/2 radius is v then by the conservation of angular momentum

$mv_0R_0=mvR_0/2$

$\implies v=2v_0$

Therefore the value of Kinetic Energy is

$KE=\frac{1}{2}mv^2$

$\implies KE=\frac{1}{2}m(2v_0)^2$

$\implies KE=2mv_0^2$

Therefore, the final value of Kinetic Energy is $2mv_0^2$