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Q.

In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When the mass is in equilibrium position, as shown in the figure, another mass m is gently fixed upon it. The new amplitude of oscillation will be :

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a

AM−mM

b

AMM+m

c

AMM−m

d

AM+mM

answer is B.

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Detailed Solution

Velocity at mean position is  =AωConserving momentum  MAω0=M+mV1⇒V1=MAω0M+m Also, New veloctiy at mean position =V1=A′ω1=A′KM+m⇒MAω0M+m=A′KM+m  here, ω0=KM⇒A′=MAKMM+m×M+mK=AM(M+m)
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