A solid rubber ball of density d and radius E falls vertically through air. Assume that the air resistance acting on the ball is F = kRV, where k is constant and V its velocity. Because of this air resistance, the ball attains a constant velocity called terminal velocity Vt after some time. Then Vt is
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a
4πR2dg3k
b
4πRd2g3k
c
4πRdg23k
d
4πRdg3k
answer is A.
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Detailed Solution
The ball attains the terminal velocity when the resultant force acting on the ball is zero. This happens when air resistance F acting upwards is exactly equal to the weight m g of the ball acting vertically downwards.∴ kRVt=mg=43πR3dgor Vt=4πR2d'g3k