Question

One mass $m$ suspended from a spring. Time period of oscillition is $T$. Now if spring is divided into $n$ pieces & these are joined in parallel order then time period of oscillation if same mass is suspended.

• A. $2\pi \sqrt{\frac{n^{2}m}{k}}$
• B. $2\pi \sqrt{\frac{n^{2}k}{m}}$
• C. $2\pi \sqrt{\frac{m}{n^{2}k}}$
• D. $2\pi \sqrt{\frac{k}{n^{2}m}}$

Answer 1

The correct option is C $2\pi \sqrt{\frac{m}{n^{2}k}}$

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

$kl=k_1\left(\frac{i}{n}\right)$

$k_1=nk$

$k_{eq}=n{k}_1=n^{2}k$

$\therefore T^1=2\pi \sqrt{\frac{m}{n^{2}k}}$

Hence,

option c is correct answer