Question 28: Gravitation

Question

If $$\mathrm{A}$$ is the areal velocity of a planet of mass $$\mathrm{M}$$, then its angular momentum is

Accepted Answer

The areal velocity of a planet is the rate at which its radius vector sweeps out area. It is given by:
$$ \mathrm{A} = \frac{1}{2} r^2 \omega $$
where $r$ is the distance from the planet to the sun and $\omega$ is its angular velocity. The angular momentum of the planet is given by:
$$ L = I \omega = Mr^2 \omega $$
where $I$ is the moment of inertia of the planet. Substituting the expression for $\omega$ from the areal velocity equation, we get:
$$ L = Mr^2 \left( \frac{2A}{r^2} \right) = 2MA $$
Therefore, the angular momentum of the planet is
2MA
. So the answer is
Option C
.

Answer

$$\frac{\mathrm{MA}}{2}$$

Answer

MA

Answer

$$2 \mathrm{MA}$$

Answer

$$\frac{\mathrm{MA}}{3}$$

Gravitation

If $\mathrm{A} is the areal velocity of a planet of mass \mathrm{M}$, then its angular momentum is

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