If the force is given by `F=at+bt^(2)` with `t` is time. The dimensions of `a` and `b` are

Options

A. `[MLT^(-4)]` and `[MLT^(-2)]`
B. `[MLT^(-3)` and `[MLT^(-4)]`
C. `[ML^(2)T^(-3)]` and `[ML^(2)T^(-2)]`
D. `[ML^(2)T^(-3)]` and `[ML^(3)T^(-4)]`

Explanation

(b) Dimension of at `=` Dimension of `F`
`[at]=[F]implies[a]=[F/t]`
`[b]=[(MLT^(-2))/T]implies[a]=[MLT^(-3)]`
Dimension of `bt^(2)=` Dimension of `F`
`[bt^(2)]=[F]=[b]=[F/(t^(2))]`
`[b]=[(MLT^(-2))/(T^(2))]implies[b]=[MLT^(-4)]`