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

Options

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

Answer

A

Explanation

In a dimensional equation, all terms must have the same dimensions. In this case, they should have the dimensions of force.
`[F]=[M^(1)L^(1)T^(-2)]`
(i) `[a]=[(F)/(t)]=[(M^(1)L^(1)T^(-2))/(T^(1))]=[M^(1)L^(1)T^(-3)]`
(ii) `[b]=[(F)/(t^(2))]=[(M^(1)L^(1)T^(-2))/(T^(2))]=[M^(1)L^(1)T^(-4)]`