Q. A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity)
A) 2 Mg
B) Mg
C) $\frac32$Mg
D) $\frac{\mathrm{Mg}}2$
Explanation
[Solution by Dr. Abubacker] At terminal velocity, weight $=$ upthrust $+$ viscous force. Upthrust $=V\rho_gg=\frac12\,(V\rho_bg)=\frac{Mg}2$. So the viscous force is $Mg-\frac{Mg}2=\frac{Mg}2$. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.