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Q.

A body of mass  m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass  m is slightly pulled down and released, it oscillates with a time period of 3s. When the mass  m is increased by 1 kg, the time period of oscillations becomes 5 s. The value of  m in kg is

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a

34

b

43

c

169

d

916

answer is D.

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Detailed Solution

Time period of spring - block system, T=2πmk For given spring, T∝mT1T2=m1m2 Here, T1=3 s,m1=m,T2=5 s,m2=m+1,m=?35=mm+1 or, 925=mm+125 m=9 m+9⇒16 m=9⇒m=916 kg
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