Question

The areal velocity and the angular momentum of the planet are related by which of the following relations?

(where $\mathrm { m } _ { \mathrm { P } }$ is the mass of the planet)

• A. $\frac { \Delta \overrightarrow { \mathrm { A } } } { \Delta \mathrm { t } } = \frac { \overrightarrow { \mathrm { L } } } { 2 \mathrm {~m} _ { \mathrm { P } } }$
• B. $\frac { \Delta \overrightarrow { \mathrm { A } } } { \Delta \mathrm { t } } = \frac { \overrightarrow { \mathrm { L } } } { \mathrm { m } _ { \mathrm { P } } }$
• C. $\frac { \Delta \overrightarrow { \mathrm { A } } } { \Delta \mathrm { t } } = \frac { 2 \overrightarrow { \mathrm { L } } } { \mathrm { m } _ { \mathrm { p } } }$
• D. $\frac { \Delta \overrightarrow { \mathrm { A } } } { \Delta \mathrm { t } } = \frac { \overrightarrow { \mathrm { L } } } { \sqrt { 2 } \mathrm {~m} _ { \mathrm { P } } }$

Answer 1

Answer: (D)

$\frac { \Delta \overrightarrow { \mathrm { A } } } { \Delta \mathrm { t } } = \frac { \overrightarrow { \mathrm { L } } } { \sqrt { 2 } \mathrm {~m} _ { \mathrm { P } } }$

Answer 2

Areal velocity and linear momentum of the planet is related by the relations.

$\frac { \Delta \overrightarrow { \mathrm { A } } } { \Delta \mathrm { t } } = \frac { \overrightarrow { \mathrm { L } } } { 2 \mathrm {~m} _ { \mathrm { p } } }$