Motion of planets in solar system is an example of conservation of

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7.Gravitation

easy

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

A

Mass

B

Linear momentum

C

Angular momentum

D

Energy

(AIIMS-2003)

Solution

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 at any instant $t,$ the planet is in position $A.$ Then area swept out be $SA$ is

$\mathrm{dA}=$ area of the curved triangle $SAB$

$\mathrm{d} \mathrm{A}=$ area of the curved triangle $\mathrm{SAB}$

$=\frac{1}{2}(A B \times S A)$

$=\frac{1}{2}(r d \theta \times r)=\frac{1}{2} r^{2} d \theta$

The instantaneous areal speed is

$\left.=\frac{d A}{d t}=\frac{1}{2} r^{2}\left(\frac{d \theta}{d t}\right)\right)=\frac{1}{2} r^{2} \omega$

Let $J$ be angular momentum, $I$ the moment of inertia and m the mass, then

$J=I \omega=m r^{2} \omega$

$=\frac{d A}{d t}=\frac{J}{2 m}=\mathrm{constant}$

Standard 11

Physics

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