n elastic balls are placed at rest on a smooth horizontal plane which is circular at the ends with radius r as shown in the figure. The masses of the balls are m,m2,m22,...,m2n−1 respectively. What is the minimum velocity which should be imparted to the first ball of mass m such that this nth ball will complete the vertical circle ?

n elastic balls are placed at rest on a smooth horizontal plane which

1.	n elastic balls are placed at rest on a smooth horizontal plane which is circular at the ends with radius r as shown in the figure. The masses of the balls are m,m2,m22,...,m2n−1 respectively. What is the minimum velocity which should be imparted to the first ball of mass m such that this nth ball will complete the vertical circle ?
Answer» $n$ elastic balls are placed at rest on a smooth horizontal plane which is circular at the ends with radius $r$ as shown in the figure. The masses of the balls are $m, \frac{m}{2}, \frac{m}{2^{2}}, . . ., \frac{m}{2^{n - 1}}$ respectively. What is the minimum velocity which should be imparted to the first ball of mass $m$ such that this $n^{t h}$ ball will complete the vertical circle ?

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