A solid sphere with uniform density and radius R is rotating initially with constant angular velocity ( ₁ ) about its diameter. After some time during the rotation its starts loosing mass at a uniform rate, with no change in its shape. The

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A solid sphere with uniform density and radius R is rotating initially with constant angular velocity ( ₁ ) about its diameter. After some time during the rotation its starts loosing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius become R / 2 is x ₁ . The value of x is ________

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Correct answer: 0

When sphere is of radius R , its mass is M , when radius is reduced to R 2 , mass will reduced to M 8 Now by conservation of angular momentum aligned & ( _ e x t =0 ) & L₁=L₂ & I₁ ₁=I₂ ₂ & ( 2 5 M R^2 ) ₁= ( 2 5 ( M 8 ) ( R 2 )^2 ) ₂ aligned ₂=32 ₁ value of x is 32 Answer is 32

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