Question

A body $B$ lies on a smooth horizontal table and another body $A$ is placed on $B$. The coefficient of friction between $A$ and $B$ is $\mu$. What acceleration given to $B$ will cause slipping to occur between $A$ and $B$ ?

• A. $\mu g$
• B. $g/\mu$
• C. $\mu /g$
• D. $\sqrt{\mu g}$

Answer 1

Answer: (A)

There is no friction between the body $B$ and surface of the table.
If the body $B$ is pulled with force $F$, then
$F=\left(m_A+m_B\right)a$
Due to this force, upper body $A$ will feel the pseudo force in a backward direction.
$f=m_A\times a$
But due to friction between $A$ and $B$, the body will not move.
Body $A$ will start moving when pseudo force is more than friction force, i.e., for slipping,
$m_{A}a=\mu m_{A}g$
$\Rightarrow a=\mu g$