question_answer 28)

                  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 c.m. (centre of mass) causing translation and a net torque at the c.m. causing rotation around an axis through the c.m. For the earth-sun system (approximating die earth as a uniform density sphere)                 (a) die 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 die earth to move around die sun.

Answer:

                  (a) \[\vec{\tau }\,={{\vec{R}}_{cm}}\times M\vec{g}\]                 If c.m. coincides with the origin, \[{{\vec{R}}_{cm}}=0\] and hence \[\vec{\tau }=0\].