Ncert Exercises & Solutions

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?

Maximum mass that the scale can read, M = 50 kg

Maximum displacement of the spring = length of the scale, l = 20 cm = 0.2 m

Time period, T = 0.6 s

Maximum force exerted on the spring, F = Mg

Where, g = acceleration due to gravity = 9.8 m / s^{2}

F = 50 \times 9.8 = 490

Spring constant, k = \frac{F}{l} = \frac{490}{0.2} = 2450 {Nm}^{- 1}

Mass m, is suspended from the balance .

Time period, T = 2 π \sqrt{\frac{m}{k}}

∴ m = {(\frac{T}{2 π})}^{2} \times k = {(\frac{0.6}{2 \times 3.14})}^{2} \times 2450 = 22.36 kg

∴ Weight of the body = mg = 22.36 \times 9.8 = 219.167 N

Hence, the weight of the body is about 219 N

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