14.8 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?

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Vishal Baghel | Contributor-Level 10

5 months ago

The 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

g = acceleration due to gravity = 9.8 m/ $s^{2}$

Hence, F = 50 $\times 9.8 N$ = 490 N

Spring constant k = $\frac{F}{l}$ = $\frac{490}{0.2}$ = 2450 N/ $m^{- 1}$

Mass m is suspended from the balance, hence time period, T = $2 π \sqrt{\frac{m}{k}}$

m = ( ${\frac{T}{2 π})}^{2} \times k$ = ( ${\frac{0.6}{2 π})}^{2} \times 2450$ = 22.34 kg

Weight = mg = 218.944 N

So the weight of the body is about 219 kg.

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