Question

A body of mass $20$g connected to a spring of spring constant k, executes simple harmonic motion with a frequency of $\left(\frac{5}{\pi }\right)$Hz. The value of spring constant is

• A. $4N{m}^{-1}$
• B. $3N{m}^{-1}$
• C. $2N{m}^{-1}$
• D. $5N{m}^{-1}$

Answer 1

Answer: (C)

$2N{m}^{-1}$

Here, $m=20g=20\times {10}^{-3}kg,v=\frac{5}{\pi }Hz$

$v=\frac{1}{2\pi }\sqrt{\frac{k}{m}}$
$k=4{\pi }^2{v}^{2}m=4{\pi }^2[\frac{5}{\pi }{]}^2\times 20\times {10}^{-3}=2N{m}^{-1}$