Question

A cart of mass $M$ has a pole on it from which a ball of mass $\mu$ hangs from a thin string attached to point P. The cart and the ball have initial velocity $v$. The cart crashes onto another cart of mass $m$ and sticks to it. The length of the string is $R$. If the smallest initial velocity from which the ball can go in the circle around point P is $v$, find the value of $v$. (Neglect friction and take $M$, $m>>$ $\mu$)

• A. $\left(\frac{M+m}{M}\right)\sqrt{4gR}$
• B. $\left(\frac{M+m}{M}\right)\sqrt{5gR}$
• C. $\left(\frac{M+m}{m}\right)\sqrt{4gR}$
• D. $\left(\frac{M+m}{m}\right)\sqrt{5gR}$

Answer 1

Answer: (D)

$\mu <<$m, M

Momentum conservation gives: $Mv=(M+m)v^{\prime }$