BITSAT2012PhysicsUnits and DimensionsActual
If the force is given by F = at + bt ² with t as time. The dimensions of a and b are
Options
- A[ MLT ⁻⁴ ] and [ MLT ⁻² ]
- B[ MLT ⁻³ ] and [ MLT ⁻⁴ ]
- C[ ML ² ~T ⁻³ ] and [ ML ² ~T ⁻² ]
- D[ ML ² ~T ⁻³ ] and [ ML ³ ~T ⁻⁴ ]
Correct answer
B. [ MLT ⁻³ ] and [ MLT ⁻⁴ ]
Step-by-step solution
Dimension of at = Dimension of F [a t]=[F] [a]= [ F t ][b]= [ M L T⁻² T ] [a]= [M L T⁻³ ] Dimension of bt ²= Dimension of F [ bt ² ]=[ F ] [ b ]= [ F t ² ][ b ]= [ ML T ⁻⁴ ~T ² ] [ b ]= [ MLT ⁻⁴ ]