Question

A spring balance has a scale that reads $0$ to $50kg.$ The length of the scale is $20cm.$ A body suspended from this balance, when displaced an released, oscillates with period of $0.6sec.$ What is the mass of the body?
($g=10m{s}^{-2}$)

• A. $219.13N$
• B. $4.2N$
• C. $1.5kg$
• D. $3.5kg$

Answer 1

The correct option is A $219.13N$

length of scale is $20$cm and it can read upto $50$ kg. hence for maximum extension correspond to maximum weight . i.e $50\times 9.8$N

Use formula,

$F=\left|Kx\right|$

Where,

$\begin{array}{c}x=20cm=20\times {10}^{-2}m\\ 50\times 9.8=K\times 20\times {10}^{-2}\\ K=2450N/m\end{array}$

We have for loaded oscillation

$\begin{array}{c}T=2\pi \sqrt{\left\{\frac{m}{K}\right\}}\\ m=T^{2}K/4{\pi }^2\\ ={\left(0.6\right)}^2\times \frac{2450}{4}\times {\left(3.14\right)}^2\\ =22.36kg\end{array}$

Weight $=mg$

$\begin{array}{c}=22.36\times 9.8\\ =219.13N\end{array}$