Question

The acceleration due to gravity on the surface of a planet, which has both mass and radius half of those of the earth is:

• A. $9.8m/s^2$
• B. $19.6m/s^2$
• C. $78.4m/s^2$
• D. $39.2m/s^2$

Answer 1

The correct option is B $19.6m/s^2$

Answer is B.
The formula for the acceleration due to gravity is based on Newton's Second Law of Motion and Newton's Law of Universal Gravitation. These two laws lead to the most useful form of the formula for calculating acceleration due to gravity: $g=\frac{Gm}{r^2}$, where g is the acceleration due to gravity, G is the universal gravitational constant, M is mass, and R is distance.
In this case, both mass and radius is half of those of the earth.
So, the acceleration due to gravity becomes $g=\frac{G\frac{m}{2}}{{\left(\frac{r}{2}\right)}^2}=2\times \frac{Gm}{r^2}=2\times 9.8m/s^2=19.6m/s^2$.
Hence, the acceleration due to gravity is $19.6m/s^2$.