Question

A trolley of initial mass
m0
is kept over a smooth surface as shown in figure. A constant force F is applied on it. Sand kept inside the trolley drains out from its floor at a constant rate of μ kg /s . After time t find

Net force on the trolley

Answer 1

The velocity of trolley after time "t" is  1 / μ loge (m0 / m0−μt)

Explanation:

• (a) Total mass of trolley and sand

m = initial mass - mass of sand drained out

or m= m0− μt

• (b) Suppose the velocity of trolley at time t is "v". Then, velocity of sand drained out is also v or relative velocity is zero. Hence, no thrust force will act in this case. Therefore,

Fnet = F

• (c) Fnet=F

ma = F

mdv / dt=F

(m0−μt)dv / dt = F

∫v - 0  dv= ∫t - 0 Fdt / m0−μt

Solving the above equation we get:

v = 1 / μ loge (m0 / m0−μt)

Thus the velocity of trolley after time "t" is  1 / μ loge (m0 / m0−μt)

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