A trolley of initial mass `m_0` 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 `(mu)kg//s`. After time t find:

(a) total mass of trolley and sand.
(b) net force on the trolley.
(c) velocity of trolley.

Answer

A

Explanation

(a) Total mass of trolley and sand
`m="initial mass-mass of sand drained out"`
or `m=m_0-mut`
(b) Let v is the velocity of trolley at time t. Then, velocity of sand drained out is also v or relative velocity is zero. Hence, no thrust force will act in this case. Therefore,
`F_(n et)=F`
(c) `F_(n et)=F`
or `ma=F` or `m(dv)/(dt)=F`
or `(m_0-mut)(dv)/(dt)=F`
`:. int_0^vdv=int_0^t(Fdt)/(m_0-mut)`
Solving this equation we get,
`v=1/mulog_e((m_0)/(m_0-mut))`