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A spring balance has a scale that reads 0 to 20 kg. The length of the scale is 10 cm. A body suspended from this balance, when displaced and released, oscillates with period of $\frac{πs}{10} .$ What is the mass of the body

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4.9 kg

9.8 kg

19.6 kg

14.7 kg

answer is A.

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Detailed Solution

Given,

mass m = 20kg

$x = 10 \times 10^{- 2}$

The time period of oscillation = $(\frac{π}{10}) s$

We know that,

$K = \frac{mg}{x}$

$K = \frac{20 \times 9.8}{10 \times 10^{- 2}}$

$K = 19.6 \times 10^{2} N / m$

Now,

$\frac{T}{2 π} = \sqrt{\frac{m}{K}}$

$m = \frac{{KT}^{2}}{4 π^{2}}$

$m = \frac{1960 \times {(\frac{π}{10})}^{2}}{4 \times π^{2}} kg$

$m = 4.9 kg$

Hence the correct answer is 4.9kg.

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