Different points in earth are at slightly different distances fro… - Vidyadip

MCQ

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 earthsun 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

The torque is zero.

Explanation:

As the earth is revolving around the sun in a circular motion (approximately in actual the path of earth around the sun is elliptical) due to gravitational attraction. When we consider the earth-sun as a single system and we are taking earth as a sphere of uniform density. Then the gravitational force (F) will be of radial nature, i.e. angle between position vector r and force F is zero. So, torque

$|\vec{\tau}|=|\vec{\text{r}}\times\vec{\text{F}}|=\text{r F}\sin0^0=0.$

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