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

Options

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

Answer

A

Explanation

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