Question

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

• A. $350.67\,N$
• B. $540.\,11\,N$
• C. $318.1\,\,N$
• D. $300.5\,N$

Answer 1

Answer: (C)

$318.1\,\,N$

Answer 2

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