Question

A cart has mass 2 metric ton and sand of 1 metric ton is inside the cart. Now a force of 10 N is applied on cart and sand starts to leak with rate of 0.5 kg/s. What is the velocity of cart when total sand has come out from the cart ?

• A. 13.86 m/s
• B. 0.06 m/s
• C. 2.81 m/s
• D. 18.01 m/s

Answer 1

Answer: (A)

Mass of the cart with sand changes then its acceleration also changes.
$a=\frac{F}{m}=\frac{F}{m_{0}-\mu t}$
where m is mass of system at time t,
$m=m_{0}-\mu t$
$a=\frac{F}{m_{0}-\mu t} \quad $or$\quad \frac{dv}{dt}=\frac{F}{m_{0}-\mu t}$
$\displaystyle \int_0^v$ dv=F$\displaystyle \int_0^t$ $\frac{dt}{m_{0}-\mu t}$
$v=\frac{F}{\mu}in\left(\frac{m_{0}}{m_{0}-\mu t}\right)$
Here F = 10 N; μ = 0.5 kg/s
m₀ = 2 metric tone
m₀ - μt = 1 metric tone
$\therefore \quad v=\frac{10}{0.5}in\left(2\right)=20\times0.693=13.86 $ m/s