Question

Figure below shows a flat car of mass 'M' on a frictionless road. A small massless wedge is fitted on it as shown. A small ball of mass 'm' is released from the top of the wedge, it slides over it and falls in the hole at distance 'l' from the initial position of the ball. Find the distance the flat car moves till the ball gets into the hole.

• A. $\frac{ml}{M+m}$
• B. $\frac{Ml}{M+m}$
• C. $\frac{m}{M}l$
• D. $\frac{M}{m}l$

Answer 1

The correct option is A $\frac{ml}{M+m}$

When the ball falls into the hole, with respect to the flat car, the ball travels as horizontal distance l. During this motion, to conserve momentum and to maintain the position of centre of mass, the car moves towards left, say by a distance x. Thus, the total distance travelled by the ball towards right is (l – x). As centre of mass remains at rest, the change in mass moments of the two (ball and car) about any point must be equal to zero. Hence
$m(l-x)=Mx\Rightarrow m=\frac{ml}{M+m}$