Question

A lead shot of $1\text{mm}$ diameter falls through a long column of glycerine. The variation of its velocity $v$ with distance covered is represented by:

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

When the lead shot falls through glycerine column, drag force $\left(F_D\right)$ and buoyant force $\left(F_B\right)$ act on it along upwards direction. However its weight $\left(mg\right)$ acts downwards.


$F_D=6\pi r\eta v$

At $t=0$, $v=0$ as the shot was just released, thus $F_D=0$.

The lead shot gets accelerated downwards and at time $t$

$a=\frac{mg-F_B-F_D}{m}$

As time elapses, distance covered, i.e. $x$ increases and the magnitude of acceleration decreases.

$\Rightarrow$ velocity of lead shot increases at a slower rate with increase in $x$, until ${\overrightarrow{F}}_{net}=0$ and a constant terminal velocity $\left(v_T\right)$ is achieved.

$\therefore$ curve in option $\left(a\right)$ is correct representation.