Question

The frequency of a sonometer wire is 100Hz. When the weights producing the tension are completely immersed in water, the frequency becomes 80Hz and on immersing the weights in a certain liquid, the frequency becomes 60Hz. The specific gravity of the liquid is

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

Hint:

Buoyant force reduces tension and hence frequency of sonometer wire.

Answer 1

The Correct Option is B

Step 1: Frequency of sonometer: f ∝ √(T)
Step 2: In water: ((80)/(100))² = (T - Uw)/(T) ⟹ (Uw)/(T) = 0.36
Step 3: In liquid: ((60)/(100))² = (T - Ul)/(T) ⟹ (Ul)/(T) = 0.64
Step 4: Specific gravity: SG = (Ul)/(Uw) = (0.64)/(0.36) ≈ 1.77