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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 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 the earth as a uniform density sphere).
Options
the torque is zero.
the torque causes the earth to spin.
the rigid body result is not applicable since the earth is not even approximately a rigid body.
the torque causes the earth to move around the sun.
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Solution
The torque is zero.
Explanation:
As the earth is revolving around the sun in a circular motion due to gravitational attraction. The force of attraction will be of radial nature i.e., the angle between position vector r and force F is zero. So, torque = |τ| = |r × F| = rFsin0° = 0.
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