Question

A force is given by F =at+bt2 where t is time,find the dimensional formula for a&b

Answer 1

Dimensional formula for force = $MLT^-^2$

The dimensional formula for "at" should also be same as that of the force.

Hence,

aT = $MLT^-^2$

a = $MLT^-^3$

Hence, the dimensional formula for "a" = $MLT^-^3$

Now,

$bt^2$ should have dimensional formula of force

Hence,

$bt^2 = MLT^-^2$

$b = MLT^-^4$

Hence, the dimensional formula for $b = MLT^-^4$