Question

Different points in earth are at slightly different distances from the sun and hence experience different forces due to gravitation. For a rigid body, we know that if various forces act at various points in it, the resultant motion is as if a net force acts on the centre of mass causing translation and a net torque at the centre of mass causing rotation around an axis through the centre of mass. For the earth-sun system (approximating the earth as a uniform density sphere)

• A. The torque is zero.
• B. The torque causes the earth to spin.
• C. The rigid body result is not applicable since the earth is not even approximately a rigid body.
• D. The torque causes the earth to move around the sun.

Answer 1

Answer: (A)

The torque is zero.

Answer 2

The earth is revolving in circular orbit around sun due to gravitational force F which acts along the radius of circular path, towards the sun i.e. angle between $\overrightarrow { \mathrm { r } }$ and is zero.

As

Torque $\vec { \tau } = \overrightarrow { \mathrm { r } } \times \overrightarrow { \mathrm { F } }$ or

$\therefore \tau = \mathrm { rF } \sin 0 ^ { \circ } = 0$