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Q.

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

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a

(M + m)MA

b

(M - m)MA

c

M(M + m)A

d

M(M - m)A

answer is C.

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Detailed Solution

According to law of conservation of momentum,                              pi=pf                         Mvmax=(m+M)v'max⇒                       v'max=Mvmax(m+M)∵                        v'max = A'ω'⇒           M·A(m+M)kM=A'k(m+M)⇒A'=AM(m+M)
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