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Question

A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from his balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body ? (Assume that π2=10,g=10m/s2)

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Solution

The scale is 20 cm long and reads up to 50 kg.
i.e., for 50 kg displacement is 20 cm.
W=Kx;W=50×10 N andx=20 cm=0.20 m

K=Wx=50×100.20=50×50=2500 N/m

Now
T=2πmKm=KT24π2

Putting values T=0.6 s,K=2500 N/m we get
m=2500×0.624×10=22.5 kg
Weight of the body =mg=22.5×10 N=225 N
Why this question?

Spring balance is such calibrated that the scale it reads is proportional to the weight of the body suspended from the spring and the proportional constant is the spring constant.

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