Question

A small metal ball of mass 'm' is dropped in a liquid contained in a vessel, attains a terminal velocity 'v'. If a metal ball of same metarial but of mass '8m' is dropped in same liquid, then the terminal velocity will be:

• A. $V$
• B. $2V$
• C. $4V$
• D. $8V$

Answer 1

The correct option is C $4V$

The formula for terminal velocity for a spherical body of radius $r$, density $\rho$, in a medium of viscosity $\eta$ and density $\sigma$ is given by:

$v=\frac{2g(\rho -\sigma )r^2}{9\eta }$

If mass is made 8 times, with material remaining same, this means that volume has also become 8 times because density is same. So, radius of sphere has become twice (because volume is directly proportional to cube of radius).

Thus, the new terminal velocity will be 4 times the original terminal velocity.