In the equation below F is a force v is a velocity and L is

In the equation below F is a force, v is a velocity, and L is a length. What are the dimensions of m?

Solution

dimensions of force are N

dimensions of velocity are m s^-1

dimensions of Length are m

==> F/m = v²/l

==> dimensions of m = F l / v²

==> N m / ( m s^-1)²

==> N m/( m² s^-2)

==> N s²/m

==> kg m s^-2 s² /m      since 1 N = 1 kg m s^-2

==> kg

Hence dimensions of m are kg