AP EAMCET2004PhysicsUnits and Dimensions
The position of a particle at time t is given by the equation x(t)= v₀ A (1-e^ A t ) v_o= constant and A>0 . Dimensions of v_o and A respectively are
Options
- A[ M ^0 LT ^0 ] and [ M ^0 ~L ^0 ~T ⁻¹ ]
- B[ M ^0 LT ⁻¹ ] and [ M ^0 LT ⁻² ]
- C[ M ^0 LT ⁻¹ ] and [ M ^0 ~L ^0 ~T ]
- D[ M ^0 LT ⁻¹ ] and [ M ^0 ~L ^0 ~T ⁻¹ ]
Correct answer
D. [ M ^0 LT ⁻¹ ] and [ M ^0 ~L ^0 ~T ⁻¹ ]
Step-by-step solution
The dimensions of x= dimensions of v₀ A Therefore, out of the given options v₀ has dimensions equal to [ M ^ LT ⁻¹ ] and A has dimensions equal to [ M ^ L ^ T ⁻¹ ] So, that aligned [v₀ ] [A] & = [ M ^ LT ⁻¹ ] [ M ^ L ^ T ⁻¹ ] =[ L ] & = dimension of x . aligned