Question

A plate of mass $M$ is placed on horizontal frictionless surface 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 direction the acceleration of the plate will be:

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

Answer 1

The correct option is A $\frac{m}{M}g$

Maximum friction between plate and block $\mu N=\mu mg$

Maximum acceleration of plate is $\frac{\mu mg}{m}$

If moving together

Acceleration $a=\frac{F}{M_t}=\frac{3\mu mg}{M+m}$

$a=\frac{3\mu mg}{M+m}>\frac{3\mu mg}{M+2m}=\frac{\mu mg}{m}$

Therefore block and plate move separately and the acceleration of the plate equal to its maximum possible acceleration $\frac{\mu mg}{m}$