Question

A body on the surface of a planet with the same radius as Earth’s weighs 10 times more than it does on Earth. What is the mass of this planet in terms of Earth’s mass?

a) 10 times Earth's mass
b) 5 times Earth's mass
c) 1/10 times Earth's mass
d) 1/5 times Earth's mass

Answer 1

The mass of the planet where a body weighs 10 times more than on Earth and has the same radius as Earth must be 10 times Earth's mass.

Step-by-step explanation:

To answer the question, we need to apply our understanding of gravitational forces. The force of gravity that a planet exerts on an object is directly proportional to the mass of the planet and inversely proportional to the square of the planet's radius. Given that the planet in question has the same radius as Earth but a body weighs 10 times more on its surface compared to Earth, we can determine the mass of the planet using the formula for gravitational force, F = G(m1*m2)/r^2, where G is the gravitational constant, m1 is the mass of the planet, m2 is the mass of the object, and r is the radius of the planet.

Since weight is the measure of the gravitational force and both planets have the same radius, the only variable that must account for the tenfold increase in weight is the mass of the planet. Therefore, if a body weighs 10 times more on the new planet, the mass of this planet must be 10 times that of Earth's, making the correct answer a) 10 times Earth's mass.