Question

A body of suspended mass $m$ is from a spring of force constant $K$. Its time period in $T$. If an additional mass $M$ is attached to m then its time period becomes $4T$.The value of mass $M$ will be

• A. $20m$
• B. $15m$
• C. $10m$
• D. $5m$

Answer 1

The correct option is B $15m$

As we know $T=2\pi \sqrt{\frac{M}{k}}$

So, $\frac{T}{4T}=\frac{2\pi \sqrt{m/k}}{2\pi \sqrt{(m+k)/k}}$

$⟹\frac{1}{16}=\frac{m}{m+M}$

$⟹M=15m$