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

Options

A. `[M L T^(-3)]` and `[M L T^(-4)]`
B. `[M L T^(-4)]` and `[M L T^(-3)]`
C. `[ M L T^(-1)]` and `[M L T^(-2)]`
D. `[ M L T^(-2)]` and `[M L T^(0)]`

Explanation

`F=at+bt^(2)`
dimensions of at and `bt^(2)` are same as that of F
`at=FrArra[T]=M^(1)L^(1)T^(-2)`
`a=M^(1)L^(1)T^(-3)`
`bt^(3)=FrArrb[T]^(2)=M^(1)L^(1)T^(-2)`
`b=M^(1)L^(1)T^(-4)`