If F denotes force and t time, then in the equation `F= at^(-1) + bt^(2)` dimensions of a and b respectively are

Options

A. `[LT^(-4)]` and `[LT^(-1)]`
B. `[LT^(-1)]` and `[LT^(-4)]`
C. `[MLT^(-4)]` and `[MLT^(-1)]`
D. `[MLT^(-1)]` and `[MLT^(-4)]`

Answer

D

Explanation

`F= at^(-1)+ bt^(2)`
`:. [a]= [F][t]= [MLT^(-2)][T]= [MLT^(-1)]`
`[b]= ([F])/([t^(2)])= ([MLT^(-2)])/([T^(2)])= [MLT^(-4)]`