Force F is given by `F=at+bt^(2)`. Where ''t'' is time. What are the dimensions of ''a'' and ''cb''?

Options

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

Answer

B

Explanation

`F=at+bt^(2)`
Using dimensions we get
`[MLT^(-2)]=a[T]=B[T]^(2)`
Dimension of `at=MLT^(-2)`
Dimension of `a=(ML^(-2))/([T])=MLT^(-3)`
Dimension of `bt^(2)=MLT^(-2)`
Dimension of `b=(MLT^(-2))/(T^(2))=MLT^(-4)`