Question:
The distance between the sun and the earth be $r$, then the angular momentum of the earth around the sun is proportional to
The distance between the sun and the earth be $r$, then the angular momentum of the earth around the sun is proportional to
Updated On: Jul 29, 2022
- $ \sqrt{r} $
- $r^3/2$
- $r$
- None of these
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The Correct Option is A
Solution and Explanation
According to Kepler's third law $T^{2} \propto r^{3} $
$\Rightarrow T \propto r^{3 / 2}$
We have $\omega=\frac{2 \pi}{T}$
$ \therefore \omega \propto r^{-3 / 2}$
Now, $L=m r^{2} \omega $
$\Rightarrow L \propto r^{2} \times r^{-3 / 2}$
$ \therefore L \alpha r^{1 / 2}$
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Concepts Used:
Momentum
It can be defined as "mass in motion." All objects have mass; so if an object is moving, then it is called as momentum.
the momentum of an object is the product of mass of the object and the velocity of the object.
Momentum = mass • velocity
The above equation can be rewritten as
p = m • v
where m is the mass and v is the velocity.
Momentum is a vector quantity and the direction of the of the vector is the same as the direction that an object.