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$).$

✓
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

Correct option: A.

The torque is zero.

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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