Question

A spring balance has a scale that reads 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this spring, when displaced and released, oscillates with a period of 0.60 s. What is the weight of the body?

Options

• 22.36 N

• 45 N

• 219.13 N

• 223.6 N

Answer 1

219.13 N

Explanation:

Given, Displacement x = 20 cm = 0.2 m,

mass = 50 kg, T = 0.60 s

using T = `2pi("m"/"k") = "m" = ("T"^2"k")/(4pi^2)` and

F = - kx `=> "k" = "F"/x = ("m" xx "g")/x = (50 xx 9.8)/0.2`

`therefore "m" = (0.6 xx 0.6 xx 50 xx 9.8)/(4 xx (3.15)^2 xx 0.2)` = 22.36 kg

∴ weight of body = mg = 22.36 × 9.8 = 219.13 N