Question

A trolley filled with sand is moving with a velocity of $v$ on a smooth horizontal surface. If the sand starts falling off at the rate of $\mu \text{kg/s}$ from the hole at its bottom, the velocity$\left(v\right)$ of the trolley as a function of time$\left(t\right)$ will be best represented by -

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Since, the horizontal surface is smooth, sand particles after leaving the trolley will continue to move with the same velocity as of the trolley at that instant.

Let us assume the velocity of the trolley at any instant of time is $v_0$.


Now,

${\overrightarrow{F}}_{ext}+{\overrightarrow{v}}_r\left(\frac{dm}{dt}\right)=m\overrightarrow{a}$

Here, ${\overrightarrow{v}}_r=0$ and also ${\overrightarrow{F}}_{ext}=0$.

So, $\overrightarrow{a}=0\Rightarrow \overrightarrow{v}=$ constant

Therefore, $v-t$ graph will be a straight line parallel to $t-$axis.

Hence, option $\left(C\right)$ is the correct answer.