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Question

A solid metallic sphere of radius r is allowed to fall freely through air. If the frictional resistance due to air is proportional to the surface area and to the square of the velocity, then the terminal velocity of the sphere is proportional to which of the following ?

A
r2
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B
r
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C
r3/2
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D
r1/2
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Solution

The correct option is D r1/2
Given that resistive force
fAV2
f=KAV2
When sphere attains terminal velocity, it is in equilibrium
mg=KAV2
43πr3ρg=K(4πr2)V2
Vr

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