A planet has a mass M1 and radius R 1. The value of acceleration due to gravity on its surface is g 1. There is another planet 2, whose mass and radius both are two times that of the first planet. Which one of the following is the acceleration due to gravity on the surface of planet 2?

The acceleration due to gravity (g) on a planet's surface is determined by the formula g = GM/R², where G is the universal gravitational constant, M is the mass of the planet, and R is its radius. For the first planet, g₁ = GM₁/R₁². For the second planet, the mass M₂ is 2M₁ and the radius R₂ is 2R₁ [1]. Substituting these values into the formula for the second planet gives g₂ = G(2M₁) / (2R₁)². Simplifying this expression results in g₂ = G(2M₁) / (4R₁²), which reduces to (1/2) * (GM₁/R₁²). Therefore, the acceleration due to gravity on the second planet is g₁/2. This demonstrates that while gravity increases linearly with mass, it decreases with the square of the radius, leading to a net reduction when both parameters are doubled.

Sources

1. [1] https://imagine.gsfc.nasa.gov/observatories/learning/swift/classroom/law_grav_guide.html