Question

A planet revolving in an elliptical orbit has :

$A).$ a constant velocity of revolution.

$B).$ the least velocity when it is nearest to the sun.

$C).$ its areal velocity directly proportional to its velocity.

$D).$ its areal velocity inversely proportional to its velocity.

$E).$ a trajectory such that the areal velocity is constant.

Choose the correct statement from the options given below :

• A. $A$ only
• B. $E$ only
• C. $D$ only
• D. $C$ only
  

Answer 1

The correct option is B $E$ only

From law of conservation of angular momentum,
$I\omega =$ constant
$\Rightarrow m{r}^2\times \frac{v}{r}=$ constant
So, $mvr=$ constant

$\Rightarrow$ Linear velocity of planet changes as radial distance from the sun changes.

$\Rightarrow$ Linear velocity is inversely proportional to the radial distance from the sun. Therefore, velocity is more when near to the sun.

$\Rightarrow$ Areal velocity, $\frac{dA}{dt}=\frac{L}{2m}=$ constant
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Hence, option $\left(B\right)$ is correct.