A solid sphere, of radius.........| FM | JEE MAIN 2019

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JEE MAIN 2019

12-04-2019 S2

Question

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 $\left(\frac{v_1}{v_2}\right)$ equals:

Select the correct option:

A

$\frac{1}{27}$

B

9

C

$\frac{1}{9}$

D

27

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$\begin{aligned} & R^3=27 r^3 \quad \Rightarrow R=3 r \\ & \frac{V_1}{V_2}=\left(\frac{R}{r}\right)^2=9\end{aligned}$

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