Question

which planet has the smallest year in earth time

Answer 1

Answer : $\shapeit{\bold{Mercury}}$

Explanation :- A very important physics concept behind of it .
when there is no external torque applied on any body , then angular momentum of body must be conserved .
means L = Iω = constant
Where I is moment of inertia and ω is angular velocity
and we also know,
ω = 2π/T , here T is time period
so, I.2π/T = constant e.g., T α I

It means time period of any rotational body directly proportional to moment of inertia of body . And you know, moment of inertia of body directly proportional to square of radius of body { when spherical body rotates about its diameter}

It means time period of spherical body is directly proportional to square of radius of body.

Now come to the point, in solar system , the smallest planet is Mercury.
Then, radius of Mercury is smallest . So, time period of Mercury is smallest.e.g., 88 days/year

Hence, Mercury has smallest year in earth time .

Answer 2

Mercury
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