Question

Compare the acceleration due to gravity on the surface of a planet, whose mass and diameter are double that of the earth, with the acceleration due to gravity on the surface of the earth.

• A. $1:2$
• B. $2:1$
• C. $3:4$
• D. $4:1$

Answer 1

The correct option is A $1:2$

Let M and R be the mass and radius of the earth respectively.

Then mass and radius of the planet will be 2M and 2R respectively.

$\Rightarrow \frac{g_{planet}}{g_{earth}}=\frac{G\left(2M\right)/(2R{)}^2}{GM/R^2}=\frac{2GM/4R}{GM/R}=\frac{1}{2}$

Hence correct answer is option $A$