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 `[MLT^(-4)]`
B. `[MLT^(-4)]` and `[MLT^(-3)]`
C. `[MLT^(-1)]` and `[MLT^(-2)]`
D. `[MLT^(-2)]` and `[MLT^(0)]`

Answer

A

Explanation

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