Question

A ball of mass 2 kg hanging from a spring oscillates with a time period $2\pi$ seconds. Ball is removed when it is in equilibrium position, then spring shortens by

• A. 10 m
• B. 5 m
• C. 20 m
• D. $2\pi m$

Answer 1

The correct option is A

10 m

$T=2\pi \sqrt{\frac{m}{k}}$

$\therefore k=\frac{4{\pi }^{2}m}{T^2}=\frac{4{\pi }^2\left(2\right)}{(2\pi {)}^2}=2N/m$

Now $mg=k{x}_0$

$\therefore x_0=\frac{mg}{k}=\frac{2\times g}{2}=gmeter=10m$