Question

The frequency of a sonometer wire is \(100\,\text{Hz}\). When the weights producing the tension are completely immersed in water, the frequency becomes \(80\,\text{Hz}\). On immersing the weights in a certain liquid, the frequency becomes \(60\,\text{Hz}\). The specific gravity of the liquid is:

• A. \(1.42\)
• B. \(1.77\)
• C. \(1.82\)
• D. \(1.21\)

Hint:

For sonometer: \[ f\propto\sqrt{T} \] Buoyancy reduces effective tension.

Answer 1

The Correct Option is B

Step 1: Frequency: \[ f\propto\sqrt{T} \]
Step 2: Tension ratios: \[ \left(\frac{80}{100}\right)^2=\frac{T_w}{T} \Rightarrow T_w=0.64T \]
Step 3: Similarly: \[ \left(\frac{60}{100}\right)^2=\frac{T_l}{T} \Rightarrow T_l=0.36T \]
Step 4: Apparent weights: \[ \frac{T-T_l}{T-T_w}=\frac{\rho_l}{\rho_w} \Rightarrow \rho_l=\frac{0.64}{0.36}\approx1.77 \]