A trolley of initial mass M 0 M_0 M 0 moves on a smooth horizontal track with speed u. Rain falls vertically into it at a constant mass rate λ. The rain has zero horizontal velocity before entering the trolley. The trolley speed after time t is:
Physics · Center of maas , Momentum and Collision · variable mass system
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Question

A trolley of initial mass M 0 M_0 M 0 ​ moves on a smooth horizontal track with speed u. Rain falls vertically into it at a constant mass rate λ. The rain has zero horizontal velocity before entering the trolley. The trolley speed after time t is:

G1 Physics · Accepted Answer

At time t, the trolley plus collected rain has mass M(t) = M0 + λt. The incoming rain has zero horizontal momentum before entering. There is no external horizontal force on the trolley-rain system. Therefore the total horizontal momentum remains equal to its initial value: [M0 + λt]v = M0u. Hence v(t) = M0u/(M0 + λt). Correct option: A.

A trolley of initial mass M 0 M_0 M 0 ​ moves on a smooth horizontal track with speed u. Rain falls vertically into it at a constant mass rate λ. The rain has zero horizontal velocity before entering the trolley. The trolley speed after time t is:

A trolley of initial mass M 0 M_0 M 0 moves on a smooth horizontal track with speed u. Rain falls vertically into it at a constant mass rate λ. The rain has zero horizontal velocity before entering the trolley. The trolley speed after time t is: