Question

If the force is given by F = at+ bt² with t as time the dimensional formula of a and b are

Answer 1

Answer:Please refer to attachment.

Answer 2

F = at +bt²

We know, by principle of homogeneity that the dimensions of all the physical questions in the left and right side of the equation must be same and only like physical quantities can be added or subtracted.

so,

[F] = [at] +[bt²]

[MLT-²] = [aT]

so,

[a] = [MLT-²]/[T] = [MLT-³]

and similarly,

[MLT-²] = [bT²]

so,

[b] =[MLT-²]/[T²] = [MLT-⁴]

Cheers!