JEE Main20245 Apr 2024Evening ShiftPhysicsUnits and DimensionsActual
What is the dimensional formula of a b⁻¹ in the equation ( P + a V ^2 )( V - b )= RT , where letters have their usual meaning.
Options
- A[ M ⁻¹ ~L ^5 ~T ^3 ]
- B[ M ^6 ~L ^7 ~T ^4 ]
- C[ ML ^2 ~T ⁻² ]
- D[ M ^0 ~L ^3 ~T ⁻² ]
Correct answer
C. [ ML ^2 ~T ⁻² ]
Step-by-step solution
[ V ]=[ b ] Dimension of b= [ L ^3 ] aligned & &[ P ]= [ a V ^2 ] & [ a ]= [ PV ^2 ]= [ ML ⁻¹ ~T ⁻² ] [ L ^6 ] aligned Dimension of a = [ ML ^5 ~T ⁻² ] ab ⁻¹= [ ML ^5 ~T ⁻² ] [ L ^3 ] = [ ML ^2 ~T ⁻² ]