Question

A spring balance has a scale that reads from $0$ to $60kg$ . The length of the scale is $30cm$ . A body suspended from this balance and when displaced and released, oscillates with a period of $0.8s,$ what is the weight of the body when oscillating?

• A. $350.67N$
• B. $540.11N$
• C. $318.1N$
• D. $300.5N$

Answer 1

Answer: (C)

Time period of the spring-mass system
$T=2\pi \sqrt{\frac{m}{k}}$ .(i)
$\Rightarrow$ For spring $mg=kx$
$k=\frac{mg}{x}=\frac{60\times 9.8}{30\times 10^{-2}}$
$=1960N/m$ ..(ii)
$\Rightarrow$ From Eqs. (i) nd (ii)
$0.8=2\pi \sqrt{\frac{m}{1960}}$
$\Rightarrow$ $\frac{0.8\times 0.8\times 1960}{4{\pi }^2}=m$
$m=31.81kg$
$w=318.1N$