Q.
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 dynamics 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) $\frac{2\mu m}{(M + m)}g$
Explanation
(a) Reaction on $m$ is $mg$. Maximum friction force by $m$ on $M$ is $\mu mg$. So, the force on $M$ is $\mu mg$ forward
Acceleration $= \frac{\mu mg}{M}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.