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Question: A plate of mass M is placed on a horizontal frictionless surface (see fig), and a body of mass m is ...

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

A

μmM\frac { \mu \mathrm { m } } { \mathrm { M } } g

B

μm(M+m)\frac { \mu \mathrm { m } } { ( \mathrm { M } + \mathrm { m } ) } g

C

2μmM\frac { 2 \mu \mathrm { m } } { \mathrm { M } } g

D

2μm(M+m)\frac { 2 \mu \mathrm { m } } { ( \mathrm { M } + \mathrm { m } ) } g

Answer

μmM\frac { \mu \mathrm { m } } { \mathrm { M } } g

Explanation

Solution

Reaction on m is mg. Maximum frictional force on m is µmg. So the force on M is µmg forward.

acceleration = μmgM\frac { \mu \mathrm { mg } } { \mathrm { M } }