A small ball of mass m is connected by an inextensible massless string of length l with another ball of mass M $$=$$ $$4m$$. They are released at $$t=0$$ with zero tension in the string from a height h as shown in the figure. The string becomes taut for the first time at $$t=lngh$$ after the mass M collides with the ground (Assume$$ all collisions to be $$elastic) . Find value of n .

Question

A small ball of mass m is connected by an inextensible massless string of length l with another ball of mass M $$=$$ $$4m$$. They are released at $$t=0$$ with zero tension in the string from a height h as shown in the figure. The string becomes taut for the first time at $$t=lngh$$ after the mass M collides with the ground (Assume$$ all collisions to be $$elastic) . Find value of n .

Infinity Learn · Accepted Answer

Before collision, the velocity of each ball is  $$V=2gh$$ in the same direction.After collision of M with ground, the velocity of M ball is  $$V=2gh$$ in the opposite direction.Relative acceleration between the two balls is zero and relative velocity of approach is $$V-(-V)=2V=22gh$$ .∴  The two balls will collide after a time  $$=relative$$ distancerelative $$velocity=l22gh$$.Since the collision is elastic, the velocity of separation is  $$22gh$$∴  The string becomes taut after same time  $$t=l22gh$$∴  Total time  will be $$2t$$ $$=$$  $$l2gh$$

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