Question

The motion of planets in the solar system is an example of conservation of

• A. mass
• B. momentum
• C. angular momentum
• D. kinetic energy

Answer 1

The Correct Option is C

Areal speed of planet is constant. From Kepler's second law of motion, a line joining any planet to the sun sweeps out equal areas in equal intervals of time. Let any instant $t$, the planet is in position $A$. Then area swept out be $SA$ is

$dA =$ area of the curved triangle $SAB$ $ =\frac{1}{2}(AB\times SA) $ $ =\frac{1}{2}(rd\theta \times r)=\frac{1}{2}{{r}^{2}}d\theta $ The instantaneous areal speed is $ \frac{dA}{dt}=\frac{1}{2}{{r}^{2}}\left( \frac{d\theta }{dt} \right)=\frac{1}{2}{{r}^{2}}\omega $ Let $J$ be angular momentum $I$ the moment of inertia and $m$ the mass, then $ J=I\omega =m{{r}^{2}}\omega $ $ \therefore $ $ \frac{dA}{dt}=\frac{J}{2m}=$ constant Hence, angular momentum of the planet is conserved.