Question

The torque of a planet about the center of the Sun is -

• A. zero
• B. negative
• C. positive
• D. dependent on mass of planet

Answer 1

Answer: (A)

The gravitational force ${\overrightarrow{F}}_g$ on the planet due to the sun and the position vector $\overrightarrow{r}$ of the planet from the sun are parallel vectors.

This is because both the gravitational force and the positional vector lie along the same line from the sun to the planet. As a rule, cthe ross product of two parallel vectors is zero.

Mathematically it is given as

Torque of force of gravity $\overrightarrow{\tau }=\overrightarrow{r}\times {\overrightarrow{F}}_a=r{F}_a\sin \theta$

Since $\overrightarrow{r}$ and ${\overrightarrow{F}}_a$ are parallel, so $\theta ={180}^{\circ }$

Or, $\therefore \tau =r{F}_a\sin {180}^{\circ }=0$