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Q.

A block P of mass m is placed on a smooth horizontal surface. A block Q of same mass is placed over the block P and the coefficient of static friction between them is $μ_{s}$ . A spring of spring constant K is attached to block Q. The blocks are displaced together to a distance A and released. The upper block oscillates without slipping over the lower block. The maximum frictional force between the block is

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a

zero

b

KA

c

KA/2

d

$μ g$

answer is C.

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Detailed Solution

Angular frequency of system,

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

Maximum acceleration, $a_{m a x} = ω^{2} A$

Frictional force between P and Q = force exerted on lower block

$= m ω^{2} A = m (\frac{K}{2 m}) A = \frac{K A}{2}$

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A block P of mass m is placed on a smooth horizontal surface. A block Q of same mass is placed over the block P and the coefficient of static friction between them is μs. A spring of spring constant K is attached to block Q. The blocks are displaced together to a distance A and released. The upper block oscillates without slipping over the lower block. The maximum frictional force between the block is