Question

A trolley of mass $300kg$ carrying a sandbag of $25kg$ is moving uniformly with a speed of $36km/h$ on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at the rate of $0.05kg/s$. Speed of the trolley when the entire sand bag is empty is

• A. 27 kmph
• B. 36 kmph
• C. 38 kmph
• D. 40 kmph

Answer 1

Answer: (B)

${\vec{F}}_{ex}+{\vec{v}}_{rel}\frac{dM}{dt}=\frac{Md\vec{v}}{dt}$
Along the direction of motion of the trolley $f_{ex}=0,{\vec{v}}_{rel}=v_{\text{sand trolley }}=(36-36)=0kmph$
$\frac{dv}{dt}=0,$ so the trolley maintains its speed $=36kmph$