Question

A body is suspended from a string of length 1 m and mass 2 g. The mass of the body required to produce a fundamental frequency of 100 Hz in the string is (Take \( g = 10 \, \text{ms}^{-2} \))

• A. 80 g
• B. 4 kg
• C. 400 g
• D. 8 kg

Hint:

Use \( f = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \), and remember linear mass density \( \mu = \frac{m}{L} \).

Answer 1

The Correct Option is D

For fundamental frequency: \[ f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}, \quad \mu = \frac{m}{L} \] Given: \( f = 100 \), \( L = 1 \), \( m = 2 \, \text{g} = 2 \times 10^{-3} \, \text{kg} \), let tension \( T = Mg \)
\[ 100 = \frac{1}{2} \sqrt{\frac{Mg}{\mu}} = \frac{1}{2} \sqrt{\frac{M \cdot 10}{2 \times 10^{-3}}} \Rightarrow 200 = \sqrt{\frac{10M}{2 \times 10^{-3}}} \Rightarrow 200^2 = \frac{10M}{2 \times 10^{-3}} \Rightarrow M = 8 \, \text{kg} \]