Question

A tiny sphere of mass $m$ and density $\rho$ is dropped in a tall jar of glycerine of density $\sigma$. When the sphere acquires terminal velocity, the magnitude of the viscous force acting on it is

• A. $\frac{mg\rho }{\sigma }$
• B. $\frac{mg\sigma }{\rho }$
• C. $mg(1+\frac{\rho }{\sigma })$
• D. $mg(1-\frac{\sigma }{\rho })$

Answer 1

The correct option is D $mg(1-\frac{\sigma }{\rho })$

$\begin{array}{c}At\\ v=v_T\\ U+F=W\\ \therefore F=W-U=W\left(1-\frac{U}{W}\right)\\ \therefore F=W\left(1-\frac{V\sigma g}{V\rho g}\right)\\ \therefore f=mg\left(1-\frac{\sigma }{\rho }\right)\\ Hence,theoptionDisthecorrectanswer.\end{array}$