Question

In the adjacent figure, a uniform disc of mass $2m$ and radius $l/2$ is lying at rest on a smooth horizontal surface. A particle ${}^{\prime }{A}^{\prime }$ of mass $m$ is connected to a light string of length $l$, whose other end is attached to the circumference of the disc. Initially string is just taut and tangential to the disc, particle $A$ is at rest. In the same horizontal plane another particle $B$ of same mass $m$ moving with velocity $v_0$ perpendicular to string collides elastically with $A$. Just after impact which of the following statements will be true.

• A. Tension in the string is $\frac{2m{v}_0^2}{5l}$
• B. Acceleration of the centre of the disc is $\frac{v_0^2}{5l}$
• C. Tension in the string is $\frac{m{v}_0^2}{5l}$
• D. Acceleration of the centre of the disc is $\frac{2v_0^2}{5l}$

Answer 1

Answer: (A), (B)

The correct options are
A Tension in the string is $\frac{2m{v}_0^2}{5l}$
B Acceleration of the centre of the disc is $\frac{v_0^2}{5l}$

For option A can be found using a simple torque balance at the time of impact, which proves that option A is correct and so the tension is $\frac{2m{v}_0^2}{5l}$

For option B, using circular motion of the disc after the moment of impact we can find the acceleration which comes out to be what is given in option B, which is $\frac{v_0^2}{5l}$.