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Q.

A long steel wire of length 'L' and radius ‘r’ is suspended from the ceiling of a room. A sphere of mass 'm' and radius 'r1 ' is attached to the lower end of the wire. the height of the ceiling is (L+2r1+l) . When the sphere is made to oscillate as a pendulum, its lowest point just touches the floor. The velocity of the sphere at the lowest point will be ( L>>(r1 ,l ) )

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a

πr2ylm−Lg

b

πr2yml−Lg

c

yπrlm

d

None

answer is A.

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Detailed Solution

T=yAeL At lowest point, Tension T=mv2L+mg v2L=yAℓmL−gv=(yπr2ℓm−gL)
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