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Oscillations

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Question : 8 of 25
Marks: +1, -0
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 this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body?
Solution:  
Here, m = 50 kg,
Maximum extension, y = 20 – 0 = 20 cm = 0.2 m
Maximum force, F = mg = 50 × 9.8 = 490 N
∴ Spring constant,
k=Fy=4900.2k = \frac{F}{y} = \frac{490}{0.2} =490×102=2450Nm−1= \frac{490 \times 10}{2} = 2450 \mathrm{Nm}^{-1}
When a body of mass M is suspended from the spring balance, it oscillates with a period of 0.6 s.
∵ Time period, T=2πMkT = 2\pi \sqrt{\frac{M}{k}} or T2=4π2MkT^{2} = 4\pi^{2} \frac{M}{k}
∴M=T2k4π2=(0.6)2×24504×(3.14)2\therefore M = \frac{T^{2} k}{4\pi^{2}} = \frac{(0.6)^{2} \times 2450}{4 \times (3.14)^{2}}
M = 22.36 kg
∴ Weight of the body,
W = Mg = 22.36 × 9.8 = 219.1 N = 22.36 kgf
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