Question

A block Q of mass m is placed on a frictionless horizontal surface. Another block P of same mass is kept on Q 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. ${\mu }_{2}mg$

Answer 1

The correct option is B $\frac{kA}{2}$

When two blocks performs simple harmonic motion together then at the extreme position( at amplitude =A)
Restoring force $F=KA=2ma\Rightarrow a=\frac{KA}{2m}$
There will be no relative motion between P and Q if pseudo force on block P is less than or just equal to limiting friction between P and Q.
i.e. $m\left(\frac{KA}{2m}\right)=Limitingfriction$
$\therefore$ Maximum friction $=\frac{KA}{2}$