99 Percentile Qs Bank for JEE MainPhysicsUnits and Dimensions
The energy of E of a system is function of time t and is given by E(t)= t- t^3 , where and are constants. The dimensions of and are
Options
- A[ ML ^2 T⁻¹ ] and [ ML ^2 T ]
- B[ LT ⁻¹ ] and [ LT ]
- C[ ML ^2 ~T ⁻³ ] and [ ML ^2 ~T ⁻⁵ ]
- D[ MLT ⁻¹ ] and [ MLT ]
Correct answer
C. [ ML ^2 ~T ⁻³ ] and [ ML ^2 ~T ⁻⁵ ]
Step-by-step solution
Energy of the system as a function of time, E(t)= t- t^3 Where, and are constant. According to principle of homogenity, dimension of t= dimension of energy i.e [ ][t]=[E] array rrr & [ ][ T ]= [ ML ^2 ~T ⁻² ] & [ ]= [ ML ^2 ~T ⁻³ ] array Again, dimension of t^3= dimension of energy array ll & [ ] [t^3 ]= [ ML ^2 ~T ⁻² ] & [ ] [ T ^3 ]= [ ML ^2 ~T ⁻² ] array [ ]= [ ML ^2 ~T ⁻⁵ ]