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

Options

A. `MLT^(-1)" and "MLT^(0)`
B. `MLT^(-3)" and "ML^(2)T^(4)`
C. `MLT^(-4)" and "MLT^(1)`
D. `MLT^(-3)" and "MLT^(-4)`

Answer

D

Explanation

`F= at+bt^(2)`
`at to "Force"=[MLT^(-2)]`
`a[T]=[MLT^(-2)]`
`implies a=[MLT^(-3)]`
Now `bt^(2) to "Force"=[MLT^(-2)]`
`b[T^2] to [MLT^(-2)]`
`b=[MLT^(-4)]`