Question

if units in two systems of measurements are in the ratio 3:4the ratio of the units of angular momentum in those two systems is

Answer 1

Given :

The ratio of units in two systems of measurements = 3 : 4

To Find :

What is the ratio of units of angular momentum in these two systems of units ?

Solution :

Since we know that angular momentum (L) is given as :

$L = mvrsin\theta$

Here m is mass of the body , v is velocity of body , r is magnitude of position vector and $\theta$ is angle made by the position vector with the horizontal .

So , ratio of the units of angular momentum can be given as :

=$\frac{[M][LT^{-1}][L]}{[M'][L'T'^{-1}][L']}$

=$[\frac{M}{M'}][\frac{L}{L'}][\frac{T^{-1}}{T'{-1}}][\frac{L}{L'}]$

=$(\frac{3}{4}\times\frac{3}{4} \times \frac{4}{3} \times \frac{3}{4} )$

= 9 :16

Hence , the ratio of units of angular momentum in these two systems of units is 9 :16 .