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A block is kept on a rough horizontal plank oscillating horizontally with an angular frequency $ω$ is in limiting equilibrium The plank is undergoing SHM of amplitude A . If the mass of the block is doubled and the frequency of oscillation is halved the amplitude of oscillation has to be to keep the block in equilibrium is

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A/2

answer is D.

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Detailed Solution

to keep the body in equilibrium the condition is maximum frictional force is equal to pseudo force i.e.

$μ m g = m ω^{2} A μ g = ω^{2} A = c o n s \tan t s o i t i s i n d e p e n d e n t o f m a s s a n d i f ω d e c r e a s e s b y 2 t i m e s A c a n b e i n c r e a s e d t o 4 t i m e s .$

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