Q 11-09-149JEE MainJEE Main 2019 (12 Apr, Shift 2)Easy
A solid sphere, of radius $R$ acquires a terminal velocity $v_1$ when falling (due to gravity) through a viscous fluid having a coefficient of viscosity $\eta$. The sphere is broken into $27$ identical solid spheres. If each of these spheres acquires a terminal velocity, $v_2$, when falling through the same fluid, the ratio $\left(\dfrac{v_1}{v_2}\right)$ equals:
Answer: (D) $9$
Each small sphere has $\dfrac1{27}$ of the volume, so radius $\dfrac R3$. Terminal velocity $v \propto r^2$:
$$\frac{v_1}{v_2} = \left(\frac{R}{R/3}\right)^2 = 9$$
Solution by Sreeraj P, M.Sc Physics