If the mass of the Earth were to double while the radius remains the same, what
Practice Questions
Q1
If the mass of the Earth were to double while the radius remains the same, what would happen to the weight of an object on its surface?
It would double
It would remain the same
It would increase by a factor of four
It would decrease by half
Questions & Step-by-Step Solutions
If the mass of the Earth were to double while the radius remains the same, what would happen to the weight of an object on its surface?
Step 1: Understand that weight is the force of gravity acting on an object.
Step 2: Know that the weight of an object depends on the mass of the Earth and the distance from the center of the Earth.
Step 3: Remember that the formula for weight (W) is W = mass of the object (m) × gravitational acceleration (g).
Step 4: Gravitational acceleration (g) is determined by the mass of the Earth (M) and the radius (R) using the formula g = G * M / R^2, where G is the gravitational constant.
Step 5: If the mass of the Earth doubles (2M) and the radius remains the same (R), the new gravitational acceleration becomes g' = G * (2M) / R^2.
Step 6: Since g' = 2 * (G * M / R^2), the new gravitational acceleration is double the original (g' = 2g).
Step 7: Therefore, if the gravitational acceleration doubles, the weight of an object on the surface also doubles.
Gravitational Force – The weight of an object is determined by the gravitational force acting on it, which is proportional to the mass of the Earth and inversely proportional to the square of the radius.
Weight and Mass Relationship – Weight is directly proportional to the mass of the object and the mass of the planet it is on.
