Question

There are small elastic balls placed at rest on a smooth horizontal surface which is circular of radius, at other end. The masses of balls are , , , ......., , respectively. The least velocity which should be provided to the first ball of mass, , such that ball completed vertical circle is

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A

B

C

D

Hard

Solution

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Correct option is A)

Let be the speed of first ball, then for a strike between first and second ball
_____ (i)

and _____ (ii)

Solving (i) and (ii)


Similarly for second and third ball

and

Solving

in this way,

For nth ball to loop

i.e.,

or

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