Simple Harmonic Motion 4 Question 9

9. 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?

(2004, 2M)

(a) $k A / 2$

(b) $k A$

(c) $\mu _s m g$

(d) Zero

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Answer:

Correct Answer: 9. (a)

Solution:

  1. Angular frequency of the system, $\omega=\sqrt{\frac{k}{m+m}}=\sqrt{\frac{k}{2 m}}$

Maximum acceleration of the system will be, $\omega^{2} A$ or $\frac{k A}{2 m}$.

This acceleration to the lower block is provided by friction.

Hence, $f _{\max }=m a _{\text {max }}=m \omega^{2} A=m \frac{k A}{2 m}=\frac{k A}{2}$



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