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A flat plate P of mass 'M' executes SHM in a horizontal plane by sliding over a frictionless surface with a frequency V. A block 'B' of mass ' m ' rests on the plate as shown in figure. Coefficient of friction between the surface of B and P is μ. What is the maximum amplitude of oscillation that the plate block system can have if the block B is not to slip on the plate :

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a

μg4π2V2

b

μg4π2V

c

μ4π2 V2 g

d

μg2π2V2

answer is A.

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Detailed Solution

fmax=μmg,amax=μg If A is the amplitude amax=Aω2=4π2AV2=μg . Therefore, A=μg4π2V2

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A flat plate P of mass 'M' executes SHM in a horizontal plane by sliding over a frictionless surface with a frequency V. A block 'B' of mass ' m ' rests on the plate as shown in figure. Coefficient of friction between the surface of B and P is μ. What is the maximum amplitude of oscillation that the plate block system can have if the block B is not to slip on the plate :