Earth needs one year to complete one revolution round the sun. If the distance between sun and earth is doubled then the period of revolution of earth will become

The correct option is 2√2 yrs.

To understand how the period of revolution of the Earth changes when the distance between the Sun and the Earth is doubled, we can use Kepler's Third Law of Planetary Motion.

Kepler's Third Law states that the square of the orbital period of a planet (T) is directly proportional to the cube of the semi-major axis of its orbit (r, which represents the average distance between the planet and the Sun):
$T^2\propto r^3$

This relationship can be written as:
$\frac{T_2}{T_1}={\left(\frac{r_2}{r_1}\right)}^{3/2}$

Let the initial orbital period of the Earth be:
$T_1=1\text{year}$
Let the initial distance between the Earth and the Sun be $r_1=r$.

According to the problem, the new distance is doubled:
$r_2=2r$

Now, substituting these values into the formula to find the new period $T_2$:
$\frac{T_2}{1}={\left(\frac{2r}{r}\right)}^{3/2}$
$T_2={\left(2\right)}^{3/2}$

We can simplify $2^{3/2}$ as follows:
$2^{3/2}=\sqrt{2^3}=\sqrt{8}=2\sqrt{2}$

Therefore, the new period of revolution of the Earth will become:
$T_2=2\sqrt{2}\text{yrs}$