Question

A plate of mass 'M' is placed on a horizontal frictionless surface and the body of mass ${}^{\prime }{m}^{\prime }$ is placed on this plate $(m<2M)$. The coefficient of friction between the body and this plate is ${}^{\prime }{\mu }^{\prime }$. If a force $3\mu mg$ is applied to the body of mass m along the horizontal, the acceleration of the plate will be

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

Answer 1

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

First we will assume that the both the block & plate will be moving together. If the common acceleration comes to out be greater than the maximum acceleration plate can have then we will treat both the block & plate separately.
Maximum Friction between plate and block: $\mu N=\mu mg$

Therefore maximum acceleration of plate is $\frac{\mu mg}{M}$If moving together:
Acceleration: $a=\frac{F}{M_t}=\frac{3\mu mg}{M+m}$
As $a=\frac{3\mu mg}{M+m}>\frac{3\mu mg}{M+2M}=\frac{\mu mg}{M}$
Therefore block and plate will move separately and the acceleration of plate will be equal to its maximum possible acceleration $\frac{\mu mg}{M}$