Question

A block of mass $m$ is placed on the top of another block of mass $M$ as shown in the figure. The coefficient of friction between them is $\mu$. Maximum acceleration of $M$ such that $M$ and $m$ move together is (there is no friction between ground and $M$)

• A. $\mu g$
• B. $\frac{g}{\mu }$
• C. $\frac{{\mu }^2}{g}$
• D. $\frac{g}{{\mu }^2}$

Answer 1

The correct option is A $\mu g$

By the free body diagram of the upper block,

as the upper block will have only frictional force and that causes the blocks to move together.

Maximum available friction to move $m$
$=\mu N=\mu mg$
Hence by the force equation on this block
$f=ma$
$\Rightarrow \mu mg=m{a}_{max}$
$\Rightarrow a_{max}=\mu g$

Option A is the correct answer