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 this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body ?

Answer 1

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/s²

F = 50 × 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,  \(T=2\pi\sqrt\frac{m}{n}\)

\(∴ m=(\frac{T}{2\pi})×k=(\frac{0.6}{2×3.14})^2×2450=22.36 \,kg\)

∴Weight of the body = mg = 22.36 × 9.8 = 219.167 N

Hence, the weight of the body is about 219 N.