A rain drop falling vertically under gravity gathers moisture from the atmosphere at a rate dm given by. kt2, where mn is the instantaneous mass, t is time and k is a constant. The dt %3D dv equation of motion of the rain drop is m- dt dm = mg dt If the drop starts falling at t=0, with zero initial velocity and initial mass m ( m, = 2 gm, k =12 gm/s' and g =1000 cm/s), the velocity v of the drop after one second is (a) 250 cm/s (b) 500 cm/s (c) 750 cm/s (d) 1000 cm/s
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