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 ?

A spring balance has a scale that reads from 0 to 50 kg. The length of

1.	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» Solution :Maximum displacement of the spring `trianglel = 20 cm = 0.2 m` Time period `T = 0.6 s, g = 9.8 ms^(-2)` Maximum force exerted on the spring `F= mg` `= 50xx 9.8= 490N` Now, force CONSTANT `k= (F)/(triangle l)` `therefore k = (490)/(0.2)= 2450 Nm^(-1)` But time period `T= 2pi SQRT((m)/(k))` `therefore (T^(2)k)/(4PI^(2))= m` `therefore ((0.6)^(2)xx2450)/(4xx(3.14)^(2))=m` `therefore m= 22.36 kg`. Weight of the body = mg `22.36xx 9.8 = 219.1N = 22.36 kgf`.