The frequency () of an oscillating liquid drop may depend upon radius () of the drop, density () of liquid and the surface tension () of the liquid as : . The values of a, b and c respectively are
- A.
- B.
- C.
- D.
Show answer and solution
Correct option: C
Solution
Using dimensional analysis, write dimensions of each quantity:
- v: T⁻¹
- r: L
- ρ: ML⁻³
- s (surface tension): MT⁻²
So: T⁻¹ = Lᵃ · (ML⁻³)ᵇ · (MT⁻²)꜀
Matching dimensions:
M: 0 = b + c → c = -b
T: -1 = -2c → c = 1/2, so b = -1/2
L: 0 = a - 3b → a = 3b = -3/2
Therefore a = -3/2, b = -1/2, c = 1/2, which matches option 3.
- v: T⁻¹
- r: L
- ρ: ML⁻³
- s (surface tension): MT⁻²
So: T⁻¹ = Lᵃ · (ML⁻³)ᵇ · (MT⁻²)꜀
Matching dimensions:
M: 0 = b + c → c = -b
T: -1 = -2c → c = 1/2, so b = -1/2
L: 0 = a - 3b → a = 3b = -3/2
Therefore a = -3/2, b = -1/2, c = 1/2, which matches option 3.
[JEE Main 2023 · 24 Jan · Shift 2]