Question

A plate of mass $M$ is placed on a horizontal frictionless surface (see figure), and a body of mass $m$ is placed on this plate. The coefficient of dynamic friction between this body and the plate is $\mu$. If a force $2 \mu\, mg$ is applied to the body of mass $m$ along the horizontal, the acceleration of the plate will be

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

Answer 1

Answer: (A)

For the body of mass $N=m g$
$f_{\max }=\mu N=\mu m g$
Since $F>\mu m g,$ the body $m$ will slide on the plate $M$, experiencing dynamic frictional force of $\mu N=\mu mg .$ Now the reaction of this force, will act on the plate.
$\Rightarrow \mu m g=M a$ or $a=\frac{\mu m g}{M}$