Question

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

• A. 4 N m${}^{-1}$
• B. 3 N m${}^{-1}$
• C. 2 N m${}^{-1}$
• D. 5 N m${}^{-1}$
• E. 2.5 N m${}^{-1}$

Answer 1

Answer: (C)

Mass (m) = 20g = 0.02 kg
Frequency (f) =$\frac{5}{\pi }Hz$
Time period of a loaded spring
$T=2\pi \sqrt{\frac{m}{k}}$
Frequency (f) = $\frac{1}{2\pi }\sqrt{\frac{k}{m}}$
$\frac{5}{\pi }=\frac{1}{2\pi }\sqrt{\frac{k}{0.02}}$
or $10=\sqrt{\frac{k}{0.02}}or100=\frac{k}{0.02}$
$\therefore k=2N{m}^{-1}$