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Q.

A long steel wire of length 'L' is suspended from the ceiling of a room. A sphere of mass 'm' and radius 'r' is attached to the lower end of the wire. The height of the ceiling is (L+e). 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 >> r,l and r is the radius of the wire)

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a

πr2eYmgL

b

πr2YmegL

 

c

πr2mYegL

d

None

answer is A.

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Detailed Solution

During oscillation, when the string is vertical, pseudo force mV2/L acting on the sphere is vertically downward so tension in the string becomes maximum.
Tmax=mg+mV2L
Elongation in the string = Height of ceiling - Length of string = (L + e) - L = e
e=TmaxLAY=mg+mV2LLπr2Y
V=πr2eYmgL
 

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