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A spring balance has a scale that reads ...

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 spring, when displaced and released, oscillates with a period of 0.6s. What is the weight of the body? When 50 kg is put, the extension of spring is 20 cm.

Text Solution

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Here, m= 50kg, Max extension, `y= 20-0- 20cm = 0.2 cm , T= 0.6s, ` Max .Force , `F= mg= 50 xx 9.8N`
`:. K= (F)/(y)= (50 xx 9.8)/(0.2)= 2450Nm^(-1)`
therefore As
`T= 2pisqrt((m)/(k)), m= (T^(2)k)/(4pi^(2))= ((0.6)^(2)xx 2450)/(4 xx (3.14)^(2))= 22.36 kg`
`:.` weight of body = `mg = 22.36 xx 9.8 = 219 .1 N`
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