You stand on the surface of a mysterious planet with a mass of 6 ×10²⁴ kg and measure the surface gravity to be 7 m/s². What must the radius of the planet be?

• A. 5.72×10¹³m
• B. 4.43×10¹⁴m
• C. 8.17×10¹²m
• D. 7.56×10⁶m

Answer: (D)

Verified step by step guidance

1. Start by recalling the formula for gravitational acceleration at the surface of a planet: $g=\frac{GM}{R^2}$, where $g$ is the surface gravity, $G$ is the gravitational constant, $M$ is the mass of the planet, and $R$ is the radius of the planet.
2. Rearrange the formula to solve for the radius $R$: $R=\sqrt{\frac{GM}{g}}$.
3. Substitute the known values into the equation: $G=\; 6.674\; \times \; 10-11m3kg-1s-2$, $M=\; 6\; \times \; 1024kg$, and $g=\; 7\; m/s2$.
4. Calculate the expression inside the square root: $\frac{GM}{g}$.
5. Finally, take the square root of the result from the previous step to find the radius $R$.