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Question

A spring balance has a scale that reads from 0 to 50kg. The length of the scale is 20cm. A block of mass m is suspended from this balance, when displaced and released, it oscillates with a period 0.5s. The value of m is (Take g = 10 m s2)

A
8 kg
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B
12kg
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C
16kg
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D
20kg
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Solution

The correct option is C 16kg
The 20cm length of the scaler reads upto 50kg.
F=mg=(50kg)(10ms2)=500N and x=20cm=0.2m
Spring constant, k=Fx=500N0.2m=2500Nm1
As T=2πmk
Squaring both sides, we get
T2=4π2mk
m=T2k4π=(0.5s)2×(2500Nm1)4×(3.14)2=16kg

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