JEE Main202315 Apr 2023Morning ShiftPhysicsUnits and DimensionsActual
The speed of a wave produced in water is given by ν = λ a g b ρ c . Where λ , g and ρ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of a , b and c respectively, are
Options
- A1 ,   - 1 ,   0
- B1 2 ,   0 ,   1 2
- C1 ,   1 ,   0
- D1 2 ,   1 2 ,   0
Correct answer
D. 1 2 ,   1 2 ,   0
Step-by-step solution
The dimensional form of velocity can be written as v = λ a g b ρ c ⇒ M 0 L T - 1 = L a L T - 2 b M L - 3 c Comparing the exponents for M , L , T , For   M ,   M c = M 0 For   L , L a + b - 3 c = L 1 For   T , T - 2 b = T - 1 So, c = 0   . . . ( i ) a + b - 3 c = 1       . . . ( i i ) - 2 b = - 1   . . . ( i i i ) From equations (i),(ii),(iii), a = 1 2 ,   b = 1 2 , c = 0