Question

A block $P$ of mass, $m$ is kept on a frictionless surface as shown in the figure. The second block of mass, $m$ is kept on it and then connected to a spring having spring constant $k.$ The two blocks are pulled by distance, $A$ . Calculate the maximum value of frictional force between two blocks if block $Q$ oscillates without slipping.

• A. $0$
• B. $kA$
• C. $\mu _{s}mg$
• D. $\frac{k A}{2}$

Answer 1

Answer: (D)

The forces acting on the masses are shown in the figure below.
Applying Newton's second law on mass $Q,$ we get-
$F-f=ma$ ...(i)
where $a$ is the acceleration at the extreme position.
Now applying
Newton's second law on mass $P,$ we get
$f=ma$ ...(ii) [acceleration is same as no slipping occurs between $Q$ and $P$ ]

$F=2ma$
$\Rightarrow a=\frac{F}{2 m}=\frac{k A}{2 m}\left[\right.\because F=kA\left]\right.$
Substituting this value of $a$ in equation (ii), we get-
$f=m\times \frac{k A}{2 m}=\frac{k A}{2}$