A cart of mass 150 kg is pulled horizontally on a frictionless surface with face 10 N. If 100 g/s sand is being dropped in the cart verticlly then find the speed of the system when cart has 100 kg snad in it.

Options

A. 10 m/s
B. 20 m/s
C. 40 m/s
D. 50 m/s

Answer

C

Explanation

`F- mu v =m (dv)/(dt)`
here `m=m_(0)+mut`
`underset(0)overset(t) int(dt)/(m_(0)+mut)overset(v)underset(0)int(dv)/(F-muv)`
`ln|1+(ut)/(m_(0))|=-ln|1-(muv)/(F)|`
`v=((Ft)/(m_(0)+mut))`
Now `F=10 N, M_(0) =150kg , mu =100xx10^(-3)kg//s=0.1 kg//s, t=1000 s`
`v=(10xx1000)/(150+100)v=40m//s`