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A solid sphere is rotating about a diameter at an angular velocity w. if it cools so that its radius reduces to 1/n of its original value. Its angular velocity becomes_____ 

(A) (ω/n) 

(B) (ω/n2

(C) nω 

(D) n2ω

1 Answer

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Best answer

Correct option: (D) n2ω

Explanation:

for solid sphere, MI = (2/5)MR2 

angular momentum is always conserved.

L1 = L2 

I1ω1 = I2ω2 

here ω1 = ω

hence

ω2 = [(I1ω) / I2]              (1)

Initial MI = I1 = (2/5)MR12 

Radius is reduced to (1/n) of original value hence R2 = (R1 / n)        (2)

hence

new MI = I2 = (2/5)MR22 

from (1)

ω2 = (ω)[{(2/5)MR12} / {(2/5)MR22}] = (ω)(R1 / R2)2 

 ω2 = ω ∙ n2            from (2)  

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