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If the distance from a mass is doubled, how does the gravitational field strengt
If the distance from a mass is doubled, how does the gravitational field strength change?
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Practice Questions
1 question
Q1
If the distance from a mass is doubled, how does the gravitational field strength change?
It doubles.
It halves.
It becomes one-fourth.
It becomes one-eighth.
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The gravitational field strength is inversely proportional to the square of the distance, so it becomes one-fourth.
Questions & Step-by-step Solutions
1 item
Q
Q: If the distance from a mass is doubled, how does the gravitational field strength change?
Solution:
The gravitational field strength is inversely proportional to the square of the distance, so it becomes one-fourth.
Steps: 8
Show Steps
Step 1: Understand that gravitational field strength (g) depends on the distance (r) from the mass.
Step 2: Remember the formula for gravitational field strength: g = G * (M / r^2), where G is the gravitational constant and M is the mass.
Step 3: Note that 'r' is the distance from the mass.
Step 4: If the distance (r) is doubled, it becomes 2r.
Step 5: Substitute 2r into the formula: g = G * (M / (2r)^2).
Step 6: Calculate (2r)^2, which is 4r^2.
Step 7: Now the formula looks like this: g = G * (M / 4r^2).
Step 8: This shows that the new gravitational field strength is one-fourth of the original strength because of the 4 in the denominator.
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