Q. A force of $6.4\ N$ stretches a vertical spring by $0.1\ m.$ The mass that must be suspended from the spring so that it oscillates with a period of $\left( \frac{\pi}{4} \right)s.$ is
A) $\left( \frac{\pi}{4} \right)kg$
B) $1kg$
C) $\left( \frac{1}{\pi} \right)kg$
D) $10kg$
Explanation
(b) Force constant of a spring is given by $F = kx$
$6.4 = k(0.1)\ $or$\ k = 64N/m$
$\because T = 2\pi\sqrt{\frac{m}{k}} \Rightarrow \frac{\pi}{4} = 2\pi\sqrt{\frac{m}{64}};\frac{m}{64} = \left( \frac{1}{8} \right)^{2};m = 1kg$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.