Question

A mass $M$ is suspended from a light spring. An additional mass $m$ added to it displaces the spring further by a distance $x$ then its time period is :

• A. T = $2\pi \sqrt{\frac{mg}{x(M+m)}}$
• B. T = $2\pi \sqrt{\frac{x(M+m)}{mg}}$
• C. T = $2\pi \sqrt{\frac{x(M+m)}{Mg}}$
• D. T = $2\pi \sqrt{\frac{Mx}{mg}}$

Answer 1

The correct option is B T = $2\pi \sqrt{\frac{x(M+m)}{mg}}$

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

$kx=mg\Rightarrow \frac{1}{k}=\frac{x}{mg}$

when weight is added, total mass $=(M+m)$

$\therefore T=2\pi \sqrt{\frac{(M+m)}{k}}=2\pi \sqrt{\frac{x(M+m)}{mg}}$