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A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is $20 \mathrm{~cm}$. A body suspended from this balance, when displaced and released, oscillates with a period of $0.6 \mathrm{~s}$. What is the weight of the body?
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Here, $m=50 \mathrm{~kg}$, max. extension $=y=20-0$
$=20 \mathrm{~cm}=0.2 \mathrm{~m}, T=0.6 \mathrm{~s}$
Force $=F=m \mathrm{~g}=50 \times 9.8 \mathrm{~N}$
$\therefore \quad k=\frac{F}{y}=\frac{50 \times 9.8}{0.2}=2450 \mathrm{~N} / \mathrm{m}$
$T=2 \pi \sqrt{\frac{m}{k}} \Rightarrow m=\frac{T^2 k}{4 \pi^2}=\frac{(0.6)^2 \times 2450}{4 \times(3.14)^2}=22.36 \mathrm{~kg}$
Weight of the body $=m \mathrm{~g}=22.36 \times 9.8=219.1 \mathrm{~N}$
$=20 \mathrm{~cm}=0.2 \mathrm{~m}, T=0.6 \mathrm{~s}$
Force $=F=m \mathrm{~g}=50 \times 9.8 \mathrm{~N}$
$\therefore \quad k=\frac{F}{y}=\frac{50 \times 9.8}{0.2}=2450 \mathrm{~N} / \mathrm{m}$
$T=2 \pi \sqrt{\frac{m}{k}} \Rightarrow m=\frac{T^2 k}{4 \pi^2}=\frac{(0.6)^2 \times 2450}{4 \times(3.14)^2}=22.36 \mathrm{~kg}$
Weight of the body $=m \mathrm{~g}=22.36 \times 9.8=219.1 \mathrm{~N}$
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