Question

A sphere of radius R and density ${\rho }_1$ is dropped in a liquid of density $\sigma$. Its terminal velocity is $v_1$. If another sphere of radius R and density ${\rho }_2$ is dropped in the same liquid, its terminal velocity will be

• A. $\left(\frac{{\rho }_2-\sigma }{{\rho }_1-\sigma }\right)v_1$
• B. $\left(\frac{{\rho }_1-\sigma }{{\rho }_2-\sigma }\right)v_1$
• C. $\left(\frac{{\rho }_1}{{\rho }_2}\right)v_1$
• D. $\left(\frac{{\rho }_2}{{\rho }_1}\right)v_1$

Answer 1

Answer: (A)

$\left(\frac{{\rho }_2-\sigma }{{\rho }_1-\sigma }\right)v_1$

Here, $6\pi \eta R{v}_1=\frac{4}{3}\pi R^3({\rho }_1-\sigma )$ ...(i)

and $6\pi \eta R{v}_2=\frac{4}{3}\pi R^3({\rho }_2-\sigma )$ ....(ii)

Eq. (ii) dividing by Eq. (i) we get

$\frac{v_2}{v_1}=\frac{({\rho }_2-\sigma )}{({\rho }_1-\sigma )}$

$u_2=\left(\frac{P_2-\sigma }{P_1-\sigma }\right)v_1$