A block of mass m is kept on a horizontal platform of mass M. The platform is doing SHM in horizontal plane with angular frequency $ω$ . There is no slipping between the block and the platform due to friction. Then

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The friction force on the block is directly proportional to the displacement of the platform from mean position.

The contact force on the block is directly proportional to the displacement of the platform from mean position.

The net contact force on the block is directly proportional to mass of block (m).

The net contact force on the platform due to the block is directly proportional to mass of plank (M).

answer is A, C.

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Detailed Solution

The particle is doing SHM because of the frictional force only. The contact force on the block is
$F = \sqrt{{(m g)}^{2} + f^{2}} = m \sqrt{g^{2} + a^{2}} = m \sqrt{g^{2} + {(ω^{2} x)}^{2}}$
This is not proportional to x but proportional to m. The contact force on the platform is F only and this is independent of m.