Question

A spherical solid ball of volume V is made of a material of density $‘s_1$’. It is falling through a liquid of density $‘s_2^{\prime }(s_2<s_1)$ assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed ‘v’, $F_{viscous}=K\cdot v^2$, The terminal speed of the ball is

• A. $\sqrt{\frac{v.g(s_1-s_2)}{K}}$
• B. $\frac{v.g.s_1}{K}$
• C. $\sqrt{\frac{v.g.s_1}{K}}$
• D. $\frac{v.g(s_1-s_2)}{K}$

Answer 1

The correct option is A $\sqrt{\frac{v.g(s_1-s_2)}{K}}$

Here, $k{v}^2=v{\rho }_{1}g-v{\rho }_{2}g$
$v=\sqrt{\frac{v({\rho }_1-{\rho }_2)g}{k}}$