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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 fig. (13). The mass oscillates on a friction less surface with time period T and amplitude A. When the mass is in equilibrium position another mass m is gently placed on it. What will be the new time period ofoscillations ?

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a

2πM+mk

b

2πM−mk

c

2πM+m2k

d

2πM−m2k

answer is A.

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Detailed Solution

When mass m is placed on mass M the new system is equivalent to a mass (M + m) attached to the spring. Hence time period of oscillationT=2πM+mk
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