Question

Two solid spheres of same metal but of mass $M$ and $8M$ fall simultaneously on a viscous liquid and their terminal velocities are $v$ and $nv$, then value of $n$ is

• A. 16
• B. 8
• C. 4
• D. 2

Answer 1

Answer: (C)

The terminal velocity is given by $v$, where $v\propto r^2(r=$ radius of the sphere).
The mass of the sphere can be given by $m=\frac{4}{3}\pi r^3\rho$, thus $m\propto r^3$.
So, according to the question, $\frac{m_1}{m_2}$
$=\frac{1}{8}={\left(\frac{r_1}{r_2}\right)}^3$
$\Rightarrow \frac{r_1}{r_2}=\frac{1}{2}$
and since, $\frac{v_1}{v_2}={\left(\frac{r_1}{r_2}\right)}^2={\left(\frac{1}{2}\right)}^2=\frac{1}{4}$
$\Rightarrow \frac{v}{nv}=\frac{1}{4}$
$\Rightarrow n=4$