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