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Q.

A small solid sphere of radius r rolls down an incline without slipping which ends into a vertical loop of radius R. Find the height above the base so that it just loops the loop

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a

52R

b

52(Rr)

c

2510(Rr)

d

2710R17r10

answer is D.

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Detailed Solution

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The minimum velocity at P, top of the loop, should b v=g(Rr)  if the sphere keeps on rolling at top v=ωR

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mgh=12mv2+12Iω2+mg(2Rr) =12mg(Rr)+1225mR22ω2+mg(2Rr)=710mg(Rr)+mg(2Rr)[ωR=v=g(Rr)]=mg10(27R17r) or h=110(27R17r)

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