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

C) 4

The terminal velocity is given by v, where v \(\propto\) r² (r = radius of the sphere).

The mass of the sphere can be given by

\(m\) = \(\frac{4}{3}\pi r^3\rho,\) Thus \(m\propto r^3\)

\(\frac{m_1}{m_2}\) = \(\frac{1}{8}\) =(\(\frac{r_1}{r^2}^3\))  \(\Rightarrow\frac{r_1}{r_2}\)= \(\frac{1}{2}\)

and since, \(\frac{v_1}{v_2}\)= (\(\frac{r_1}{r_2}\))²  =  \(\frac{1}{4}\)

\(\Rightarrow \frac{v}{nv} = \frac{1}{4}\)

\(\Rightarrow n=4\)