The ratio of the weights of an object on the Earth's surface to that on the surface of a planet is 9:4 where both planets have same density. The mass of the planet is (1/9) th of that of the Earth. If R' is the radius of the Earth, what is the radius of the planet?

Question

The ratio of the weights of an object on the Earth's surface to that on the surface of a planet is 9:4 where both planets have same density. The mass of the planet is (1/9) th of that of the Earth. If R' is the radius of the Earth, what is the radius of the planet? (A) (R/9) (B) (R/4) (C) (R/3) (D) (R/2)

Tardigrade Admin · Accepted Answer

w1=(GM1 m/R12) w2=(GM2 m/R22) (w1/w2)=(M1/M2)((R2/R1))2 (4/9)=(1/9)((R2/R1))2 (R1/R2)=(1/2)

Q. The ratio of the weights of an object on the Earth's surface to that on the surface of a planet is $9 : 4$ where both planets have same density. The mass of the planet is $\frac{1}{9}$ th of that of the Earth. If R' is the radius of the Earth, what is the radius of the planet?

$\frac{R}{9}$

$\frac{R}{4}$

$\frac{R}{3}$

$\frac{R}{2}$

$w_{1} = \frac{G M _{1} m}{R _{1}^{2}}$
$w_{2} = \frac{G M _{2} m}{R _{2}^{2}}$
$\frac{w _{1}}{w _{2}} = \frac{M _{1}}{M _{2}} (\frac{R _{2}}{R _{1}})^{2}$
$\frac{4}{9} = \frac{1}{9} (\frac{R _{2}}{R _{1}})^{2}$
$\frac{R _{1}}{R _{2}} = \frac{1}{2}$

Q. The ratio of the weights of an object on the Earth's surface to that on the surface of a planet is 9:4 where both planets have same density. The mass of the planet is 91​ th of that of the Earth. If R' is the radius of the Earth, what is the radius of the planet?

9R​

4R​

3R​

2R​