Question

A block P of mass m is placed on a frictionless horizontal surface. Another block Q of same mass is kept on P and connected to the wall with the help of a spring of spring constant k as shown in the figure. ${\mu }_s$ is the coefficient of friction between P and Q. The blocks move together performing SHM of amplitude A. The maximum value of the friction force between P and Q is:

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

Answer 1

The correct option is B

$\frac{kA}{2}$

Here, $\omega =\sqrt{\frac{k}{m+m}}=\sqrt{\frac{k}{2m}}$
Frictional force ($f$) will provide the required restoring force to block P and its value will be maximum at the extreme position.
So, $f_{max}=m{\omega }^{2}A=m\times \frac{k}{2m}\times A=\frac{kA}{2}$