Question

An object has a weight of 300 N, if the object is taken to Planet P that has 2 times the

mass of the Earth but is 1/2 the size (distance) of the Earth. What is the weight of the
object on Planet P?
A) 0 N
B) 1200 N
C) 600 N
D) 2400 N
E) 300 N

Answer 1

Doubling the mass of an object doubles its weight while doubling its distance from the center of the Earth reduces its weight fourfold. In the given scenario, the weight of the object on Planet P is calculated by considering the change in the acceleration due to gravity. The weight of the object on Planet P is 1200 N.

Step-by-step explanation:

The weight of an object is determined by the gravitational force acting on it. Doubling the mass of an object doubles its weight because weight is directly proportional to mass. However, doubling the distance from the center of the Earth reduces the weight of the object fourfold because weight is inversely proportional to the square of the distance.

In the given scenario, the mass of Planet P is 2 times that of the Earth, but its size (distance) is only 1/2 of the Earth. Therefore, the weight of the object on Planet P can be calculated using the equation:

Weight on Planet P = (Mass of Object on Planet P) × (Acceleration due to Gravity on Planet P)

Since the mass of the object remains the same, only the acceleration due to gravity changes. Given that the size of Planet P is 1/2 of the Earth, the acceleration due to gravity on Planet P would be 4 times that of Earth since it is inversely proportional to the square of the distance. Therefore, the weight of the object on Planet P would be 4 times its weight on Earth.

Hence, the weight of the object on Planet P would be 4 × 300 N = 1200 N.