Planet A has double the radius than that of Planet B. If the mass of Planet A is 4 times heavier than the mass of Planet B, which of the following statements regarding weight of an object is correct?

The weight of an object on a planet is determined by the surface gravitational acceleration (g), which is calculated using the formula g = GM/R², where G is the gravitational constant, M is the planet's mass, and R is its radius. Weight is directly proportional to the planet's mass and inversely proportional to the square of its radius. For Planet A, the mass (M_A) is 4 times that of Planet B (M_B), and the radius (R_A) is 2 times that of Planet B (R_B). Substituting these into the formula for Planet A gives g_A = G(4 * M_B) / (2 * R_B)² = G(4 * M_B) / (4 * R_B²) = G * M_B / R_B². This result is identical to the surface gravity of Planet B (g_B). Since the gravitational acceleration is the same on both planets, the weight of an object (W = mg) will be the same on both Planet A and Planet B.

Sources

1. [1] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 5: Exploring Forces > A step further > p. 75