Question

Let a star be much brighter than our sun but its mass is same as that of sun. If our earth has average life span of a man as 70 years, then on earth like planet of this star system at double the distance between our earth and sun will have an average life span of a man as

• A. 25 planet years
• B. 20 planet years
• C. 70 planet years
• D. 15 planet years

Answer 1

Answer: (A)

25 planet years

We have the time period of revolution as $T=\frac{2\pi }{\omega }=\frac{2\pi R}{v}$.
Here v is the orbital speed which is given as $v=\sqrt{\frac{GM}{R}}$
Thus we get $T=2\pi R\times \sqrt{\frac{R}{GM}}$
Thus we get $\frac{T_1}{T_2}={\frac{R_1}{R_2}}^{3/2}$
As the ratio of the radii is $1:2$, thus we get the ratio of the time periods as $1:2\sqrt{2}$.
Thus the time period of revolution of the planet is $2\sqrt{2}$ times the time period of earth. Thus we get the life span of the man on that planet as $\frac{70}{2\sqrt{2}}=24.75\approx 25years$