Question

a ball is moved from earth to a planet that has a gravitational acceleration that is double that of earth. how does the gravitational force on the ball when it is on the new planet compare to the gravitational force on the ball when it is on earth?
a the gravitational force on the ball on the new planet is double the force on the ball when it is on earth.
b the gravitational force on the ball on the new planet is half the force on the ball when it is on earth.
c the gravitational force on the ball on the new planet is the same as the force on the ball when it is on earth.
d the gravitational force on the ball on the new planet is one - fourth the force on the ball when it is on earth.

Explanation:

Step1: Recall the formula for gravitational force

The gravitational force (weight) on an object is given by \( F = mg \), where \( m \) is the mass of the object and \( g \) is the acceleration due to gravity.

Step2: Analyze the mass and gravity change

The mass \( m \) of the ball remains constant (mass is an intrinsic property). Let the acceleration due to gravity on Earth be \( g_E \), so the force on Earth \( F_E = mg_E \). On the new planet, the acceleration due to gravity \( g_P = 2g_E \) (double that of Earth).

Step3: Calculate the force on the new planet

The force on the new planet \( F_P = mg_P \). Substitute \( g_P = 2g_E \) into the formula: \( F_P = m(2g_E) = 2(mg_E) \). But \( F_E = mg_E \), so \( F_P = 2F_E \).

Answer:

A. The gravitational force on the ball on the new planet is double the force on the ball when it is on Earth.