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Question

Two hail stones iron the form of a sphere with radii in the ratio 1:2, fall from a great height through the atmosphere. What will be the ratio of their momenta when they attain their respective terminal velocities?

A
1:16
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B
1;32
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C
1:1
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D
1;4
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Solution

The correct option is B 1;32The terminal velocity is attained when gravitational force is equal and opposite is given byv=2r2(ρ−σ)g9η. . . . . . . (1)v∝r2.v1v2=r21r22v1v2=1222=14Mass, m=ρ43πr3. . . . . .(2)m∝r3m1m2=(r1r2)3m1m2=(12)3=18ratio of momentum,P1P2=m1m2.v1v2P1P2=18.14=132P1:P2=1:32The correct option is B.

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