If F denotes force and t time, then in the equation F = `at^(-1) + bt^(2)`, the 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] and [MLT^(-4)]`

Answer

D

Explanation

By the principal of dimensions homogenety
`F = at^(-1)`
`[MLT^(-2)] = a[T^(-1)]`
`therefore" "a = [MLT^(-1)]`
Similarly for `b = [MLT^(-4)]`
So, `[MLT^(-1)], [MLT^(-4)]`