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  • 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.

Q. 14.8 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?

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Spring constant of the spring is given by

\\k=\frac{Weight\ of\ Maximum\ mass\ the\ scale\ can\ read}{Maximum\ displacement\ of\ the\ scale}\\ k=\frac{50\times 9.8}{20\times 10^{-2}}\\ k=2450\ Nm^{-1}

The time period of a spring attached to a body of mass m is given by

\\T=2\pi \sqrt{\frac{m}{k}}\\ m=\frac{T^{2}k}{4\pi ^{2}}\\ m=\frac{(0.6)^{2}\times 2450}{4\pi ^{2}}\\ m=22.34\ kg\\ w=mg\\ w=22.34\times 9.8\\ w=218.95\ N

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Sayak

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