Question

A plate of mass $M$ is placed on a horizontal frictionless surface and the body of mass $m$ is placed on this plate. The coefficient of friction between the body and this plate is $\mu$. If a force $3\mu$ $mg$ is applied to the body of mass $\left(m\right)$ along the horizontal, the acceleration of the plate will be:

• A. $\frac{\mu mg}{M}$
• B. $\frac{\mu mg}{(M+m)}$
• C. $\frac{3\mu mg}{\left(M\right)}$
• D. $\frac{2\mu mg}{(m+M)}$

Answer 1

The correct option is A $\frac{\mu mg}{M}$

First we will assume that both block and plate will be moving together. If the common acceleration comes out to be greater than the maximum acceleration plate can have then we will treat block and plate seperately.

$\mu N=\mu mg\left(maxfrictionbetweenblockandplate\right)maxaccelerationofplateis\frac{\mu mg}{M}Butiftheyaremovingtogetherthen,a=\frac{F}{M}=\frac{3\mu Mg}{M+m}a=\frac{3\mu Mg}{M+m}>\frac{F}{M}Henceblockandplatewillmoveseperatelyandaccelerationofplatewillbeequaltoitsmaximumpossibleacceleration\frac{\mu mg}{M}$