If the radius of the Earth were to increase by 50%, what would happen to the weight of an object on its surface?
Practice Questions
1 question
Q1
If the radius of the Earth were to increase by 50%, what would happen to the weight of an object on its surface?
It increases by 50%
It increases by 25%
It decreases by 25%
It remains the same
Weight is inversely proportional to the square of the radius. If radius increases by 50%, weight decreases by 25%.
Questions & Step-by-step Solutions
1 item
Q
Q: If the radius of the Earth were to increase by 50%, what would happen to the weight of an object on its surface?
Solution: Weight is inversely proportional to the square of the radius. If radius increases by 50%, weight decreases by 25%.
Steps: 9
Step 1: Understand that weight is the force of gravity acting on an object.
Step 2: Know that the force of gravity depends on the mass of the Earth and the distance from the center of the Earth (which is the radius).
Step 3: Remember that weight is inversely proportional to the square of the radius. This means that if the radius increases, the weight decreases.
Step 4: Calculate the new radius. If the original radius is R, a 50% increase means the new radius is 1.5R.
Step 5: Use the formula for weight: Weight ∝ 1/(radius^2). So, the original weight is proportional to 1/(R^2) and the new weight is proportional to 1/((1.5R)^2).
Step 6: Calculate the new weight: (1.5R)^2 = 2.25R^2. Therefore, the new weight is proportional to 1/2.25R^2.
Step 7: Compare the original weight (1/R^2) to the new weight (1/2.25R^2). This shows that the new weight is 1/2.25 times the original weight.
Step 8: Calculate the decrease in weight: 1 - (1/2.25) = 1 - 0.4444 = 0.5556, which is approximately a 55.56% decrease in weight.
Step 9: Conclude that if the radius of the Earth increases by 50%, the weight of an object on its surface decreases significantly.
