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?

Given

Mass of the spring balance,M = 50 kg,

Length of the scale,Y = 20 cm = 0.2 m,

Period of oscillation,T = 0.60 seconds.

We know,

F = ky or M = ky i.e

Mass ×acceleration due to gravity = Spring constant × Length of scale.

Hence, k = Mg/0.2

= 50×9.8/0.2 N/m

= 2450 N/m

Now, T = 2π√m/k

T^{2} = 4π^{2}m/k

Hence, m = T^{2}k/4π^{2}

Substituting the values we get,

m = kg = 22.3 kg

Hence, mg = 218.5 N = 22.3 kgf.

11