Q: A block P of mass m is placed on a horizontal frictionless plane. A second block of same mass m is placed on it and is connected to a spring of spring constant k, the two blocks are pulled by a distance A. Block Q oscillates without slipping. What is the maximum value of frictional force between the two blocks ?

(a) kA/2

(b) kA

(c) μ_{s} m g

(d) Zero

Ans: (a)

Sol: Angular frequency of the system $\large \omega = \sqrt{\frac{k}{m+m}}$

$\large \omega = \sqrt{\frac{k}{2 m}}$

Maximum acceleration of the system is

$\large a_{max}= \omega^2 A = \frac{k A}{2 m}$

This acceleration to the lower block is provided by friction

$\large f_{max} = m a_{max}$

$\large f_{max} = m (\frac{k A}{2 m}) = \frac{k A}{2}$