If Force (F) and time (t) are related by the equation `F=at+bt^(2)` then the dimensions of a and b are respectively given by

Options

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

Answer

c

Explanation

`F=at+bt^(2)`
As the dimensions of all terms in a dimensional equation, must be the same.
`therefore [a]=[(F)/(t)]=[(M^(1)L^(1)T^(-2))/(T^(1))]=[M^(1)L^(1)T^(-3)]`
and `[b]=[(F)/(t^(2))]=[(M^(1)L^(1)T^(-2))/(T^(2))]=[M^(1)L^(1)T^(-4)]`