Question

A force is given by
$f = at + {bt}^{2} (\: where \: t \: is \: the \: time)$
find dimensions of a and b

Answer 1

The dimension formula of force is - M¹L¹T^-2
Then the dimension formula of at and bt should be equal to this
So at =M¹L¹/TO
If t is the time then
aT =M¹L¹/T²
A=M¹L¹/T³
And for be it will same
So
bt=M¹L¹/T²
bT²=M¹L¹/T²
b=M¹L¹/T⁴