Question

In the figure shown a block A of mass m is kept on block B of mass m.A is given a velocity towards right as shown. The coefficient of friction between A and B is $\frac{3\mu }{2}$ and that between B and ground is $\mu$.

• A. B will accelerate towards right with acceleration $\frac{\mu g}{2}$.
• B. B will accelerate towards left with acceleration $\frac{\mu g}{2}$.
• C. B will not accelerate at all.
• D. B will move towards right with acceleration $\mu g$.

Answer 1

The correct option is C B will not accelerate at all.

The frictional force acts on block A in the direction opposite to the velocity of the block $=\frac{3}{2}\mu mg$

The reaction pair of this force acts on the block B.

The maximum frictional force that acts on the bottom surface of the block B $=\mu (mg+mg)=2\mu mg>\frac{3}{2}\mu mg=$ Frictional force acting on upper surface of block B.

Thus the force acting on the lower surface balances the force acting on the upper surface of the block B.

Thus the net force acting on the block is zero.

Hence, B will not accelerate at all.