A spherical rain drop of radius R and mass M falls vertically through a cloud la

Question

A spherical rain drop of radius R and mass M falls vertically through a cloud layer. The drop enters the cloud layer at a height H from the ground and exits the cloud at a height h. While inside the cloud the drop accumulates water molecules so that its mass and size grow with time. The mass of the ram drop at time t when inside the cloud is given as follows: m(t) = M+ at with t = 0 at the tune the drop enters the cloud, and a the rate at which water molecules accumulate. Write an expression for the speed of the ram drop as a function of tune when it is inside the cloud if it has a speed of v_0 immediately before entering the cloud.

Explanation / Answer

Here the effectie force acting is gravitational force.

By momentum equation,

mv = Mvo + gt

[M+at]v =  Mvo + gt

v(t) =  [Mvo + gt]/[M+at] where g is acceleration due to gravity, if ignored, gt term will not be there..

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