COMEDK2012PhysicsUnits and Dimensions
If x=a t+b t² , where x is measured in metre and t in second, then the dimension of (b / a) is
Options
- A[ LT ⁻² ]
- B[ LT ⁻¹ ]
- C[ T ]
- D[ T ⁻¹ ]
Correct answer
D. [ T ⁻¹ ]
Step-by-step solution
Given, x=a t+b t² Here, x is measured in metre ( m ) and t is in second ( s ) . So, for dimensional consistency of equation, Dimensions of a=[a]= [x] [t] = [L] [T] = [L⁻¹ ] Similarly, for b,[b]= [x] [t² ] = [L] [ T ² ] = [ LT ⁻² ] Dimensions of [ b a ]= [L ~T ⁻² ] [L ~T ⁻¹ ] = [ T ⁻¹ ]