The displacement of a particle moving along x-axis with respect to time t is `x = at + bt^(2) - ct^(3)` The dimensions of care

Options

A. `[T^(-3)]`
B. `[LT^(-2)]`
C. `[LT^(-3)]`
D. `[LT^(3)]`

Answer

C

Explanation

`x= at+ bt^(2)-ct^(3)`
Each term on RHS must have dimensions of x.
`:. [ct^(3)]= [x]` or `[c]= ([x])/([t^(3)])= ([L])/([T^(3)])= [LT^(-3)]`