Question

If the Earth-Sun distance is held constant and the mass of the Sun is doubled, then the period of revolution of the earth around the Sun will change to ____________.

पर्याय

• (1/2) year

• ${\displaystyle 1/\sqrt{2}}$ year

• ${\displaystyle \sqrt{2}}$

• 2 years

Answer 1

If the Earth-Sun distance is held constant and the mass of the Sun is doubled, then the period of revolution of the earth around the Sun will change to ${\displaystyle 1/\sqrt{2}}$ year.

Explanation:

${\displaystyle \text{T}=2\pi \sqrt{\frac{{\text{r}}^3}{\text{GM}}}}$

${\displaystyle \therefore \text{T}\propto \frac{1}{\sqrt{\text{M}}}}$     ${\displaystyle \therefore \frac{{\text{T}}_2}{{\text{T}}_1}=\sqrt{\frac{{\text{M}}_1}{{\text{M}}_2}}}$

${\displaystyle \therefore {\text{T}}_2=1\times \sqrt{\frac{1}{2}} \text{year}}$