Question

In planetary motion the areal velocity of position vector of a planet depends on angular velocity $( \omega )$ and the distance of the planet from sun (r). If so the correct relation for areal velocity is

• A. $\frac { d A } { d t } \propto \omega r$
• B. $\frac { d A } { d t } \propto \omega ^ { 2 } r$
• C. $\frac { d A } { d t } \propto \omega r ^ { 2 }$
• D. $\frac { d A } { d t } \propto \sqrt { \omega r }$

Answer 1

Answer: (C)

$\frac { d A } { d t } \propto \omega r ^ { 2 }$

Answer 2

$= \frac { m v r } { 2 m }$ $= \frac { 1 } { 2 } \omega r ^ { 2 }$

[As Angular momentum $L = m v r$and v = rω ]

∴ $\frac { d A } { d t } \propto \omega r ^ { 2 }$.