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A block P of mass m is placed on a horizonal frictionless plane. A second block of same mass m is placed on it and is connected to a spring of spring consant K, the two blocks are pulled by distance A. Block Q oscillates without slipping what is the maximum value of frictional force between blocks

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μ_{s} mg

Zero

\frac{KA}{2}

answer is A.

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Detailed Solution

Angular frequency

ω = \sqrt{\frac{K}{m + m}} = \sqrt{\frac{K}{2 m}}

Maximum acceleration of the system $= \frac{KA}{2m}$

This acceleration to the lower block is provided by friction

$f_{\max} = {ma}_{\max}$

$= m ω^{2} A = m (\frac{KA}{2m})$

$= \frac{KA}{2}$

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