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

Options

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

Answer

C

Explanation

The displacement of a particle moving along x-axis with respect to time t
`x=at+bt^(2)-ct^(3)`
Dimension of `ct^(3)` = Dimension of x
`[ct^(3)]=[x]`
or `[c]=([L])/([T^(3)])`
Dimensions of `c=[LT^(-3)]`