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Q.

They are small elastic balls placed at rest on a smooth horizontal surface which are circulated at the extremes with radius 2m. The masses of balls are M,M2,M22....M2n−1 . Find the least velocity which should be provided to the first ball of mass m such that 5th ball completes a vertical circle (nearly)  [in  ms−1] .

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answer is 3.

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Detailed Solution

V2=2m1u1m1+m2 V2=2M(M+M2)u=43u V3=2M2(M2+M4)×43u=(43)2uBetween M4  and M8 V4=(43)3uSimilarly   V5=(43)4uGiven V5=5gR=5×2×10=1010=(43)4u⇒u=3 m/s
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