Question

For a body in simple harmonic motion, the relation between force \( F \) (in Newton) acting on the body and its displacement \( y \) (in metre) is given as \( F + 3y = 0 \). If the time period of oscillation of the body is \( \pi \) s, then its mass is

• A. 12 kg
• B. 750 g
• C. 1500 g
• D. 200 g

Hint:

In SHM, the force-displacement relation is \( F = -ky \), and the time period is \( T = 2\pi \sqrt{\frac{m}{k}} \). Rearranging this lets you solve for unknown mass or spring constant easily.

Answer 1

The Correct Option is B

Step 1: Use the SHM equation form
\[ F = -ky \Rightarrow -3y = -ky \Rightarrow k = 3\, \text{N/m} \] Step 2: Time period of SHM: \[ T = 2\pi \sqrt{\frac{m}{k}} \Rightarrow \pi = 2\pi \sqrt{\frac{m}{3}} \Rightarrow \frac{1}{2} = \sqrt{\frac{m}{3}} \Rightarrow \frac{1}{4} = \frac{m}{3} \Rightarrow m = \frac{3}{4} = 0.75\,\text{kg} = 750\,\text{g} \]