Question

If a spring has time period $T$, and is cut into $n$ equa parts, then the time period of each part will be

• A. $T\sqrt{n}$
• B. $T/\sqrt{n}$
• C. $nT$
• D. $T$

Answer 1

Answer: (B)

For a spring, $T=2\pi \sqrt{\frac{m}{k}}$
For each piece, spring constant $=nk$
$\therefore T^{\prime }=2\pi \sqrt{\frac{m}{nk}}$
$\therefore T^{\prime }=2\pi \sqrt{\frac{m}{k}}\times \frac{1}{\sqrt{n}}=\frac{T}{\sqrt{n}}$