Question

If the distance of the earth from Sun is $1.5 \times 10^6 km$. Then the distance of an imaginary planet from Sun, if its period of revolution is $2.83$ years is :

• A. $6 \times 10^6 km$
• B. $3 \times 10^6 km$
• C. $6 \times 10^7 km$
• D. $3 \times 10^7 km$

Answer 1

Answer: (B)

$ T ^2 \propto R ^3 \Rightarrow\left(\frac{ T _1}{ T _2}\right)^2=\left(\frac{ R _1}{ R _2}\right)^3 $
$ \Rightarrow\left(\frac{1}{2.83}\right)^2=\left(\frac{1.5 \times 10^6}{ R _2}\right)^3 $
$ \Rightarrow R _2=\left[(2.83)^2 \times\left(1.5 \times 10^6\right)^3\right]^{1 / 3} $
$ =8^{1 / 3} \times 1.5 \times 10^6=3 \times 10^6 km $