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

The correct option is C $4$

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, $\frac{m_1}{m_2}=\frac{1}{8}={\left(\begin{array}{c}\frac{r_1}{r_2}\end{array}\right)}^3$

$\Rightarrow \frac{r_1}{r_2}=\frac{1}{2}$

and since, $\frac{v_1}{v_2}={\left(\begin{array}{c}\frac{r_1}{r_2}\end{array}\right)}^2={\left(\begin{array}{c}\frac{1}{2}\end{array}\right)}^2=\frac{1}{4}$

$\Rightarrow \frac{v}{nv}=\frac{1}{4}\Rightarrow n=4$