NEET2006PhysicsUnits and DimensionsActual
A force F is given by F=a t+b t^2 , where, t is time. What are the dimensions of a and b ?
Options
- A[ MLT ⁻¹ ] and [ MLT ^0 ]
- B[ MLT ⁻³ ] and [ ML ^2 ~T ^4 ]
- C[ MLT ⁻⁴ ] and [ MLT ^1 ]
- D[ MLT ⁻³ ] and [ MLT ⁻⁴ ]
Correct answer
D. [ MLT ⁻³ ] and [ MLT ⁻⁴ ]
Step-by-step solution
Force F=a t+b t^2 From principle of homogeneity, Dimensions of a t= dimensions of F Dimensions of a= [F] [t] = [ MLT ⁻² ] [ T ] = [ MLT ⁻³ ] Similarly, dimensions of b= [F] [t^2 ] = [ MLT ⁻² ] [ T ^2 ] = [ MLT ⁻⁴ ]