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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 in $N$?
$349$
$219$
$251$
$289$
Solution
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, $F=M g$
Where, $g=$ acceleration due to gravity $=9.8 \,m / s ^{2}$
$F=50 \times 9.8=490$
Spring constant, $k=\frac{F}{l}=\frac{490}{0.2}=2450 \,Nm ^{-1}$
Mass $m,$ is suspended from the balance.
Time period, $T=2 \pi \sqrt{\frac{m}{k}}$
$\therefore m=\left(\frac{T}{2 \pi}\right)^{2} \times k=\left(\frac{0.6}{2 \times 3.14}\right)^{2} \times 2450=22.36 \,kg$
Weight of the body $=m g=22.36 \times 9.8=219.167\, N$
Hence, the weight of the body is about $219\; N$
