1. According to the inverse square law of gravitation, the gravitational force between two masses is proportional to:
A.
The square of the distance between them
B.
The inverse of the distance between them
C.
The inverse square of the distance between them
D.
The distance cubed between them
Correct Answer:
The inverse square of the distance between them
Explanation:
The gravitational force varies as F ∝ 1/r², where r is the distance between the centers of the two masses.
2. If the distance between two masses is doubled, their gravitational force becomes:
A.
Twice as large
B.
Half as large
C.
One-fourth as large
D.
Four times as large
Correct Answer:
One-fourth as large
Explanation:
Since force is inversely proportional to the square of distance, doubling the distance gives F' = F/2² = F/4.
3. If the distance between two masses is reduced to half, the gravitational force becomes:
A.
One-fourth of the original force
B.
Half of the original force
C.
Twice the original force
D.
Four times the original force
Correct Answer:
Four times the original force
Explanation:
When distance becomes r/2, the force becomes proportional to 1/(r/2)² = 4/r², so it is four times greater.
4. A gravitational force is 20 N when the separation between two masses is r. What is the force when the separation becomes 2r?
A.
5 N
B.
10 N
C.
40 N
D.
80 N
Correct Answer:
5 N
Explanation:
At twice the distance, the force becomes one-fourth. Therefore, the new force is 20/4 = 5 N.
5. A gravitational force between two masses is 8 N at a certain distance. What will it be when the distance is tripled?
A.
24 N
B.
8/3 N
C.
8/9 N
D.
72 N
Correct Answer:
8/9 N
Explanation:
Tripling the distance reduces the force by a factor of 3² = 9. Thus, the new force is 8/9 N.
6. If the distance between two masses changes from r to 4r, the gravitational force changes by a factor of:
A.
4
B.
8
C.
16
D.
1/16
Correct Answer:
1/16
Explanation:
Because F ∝ 1/r², replacing r with 4r gives F' = F/(4²) = F/16.
7. At what distance will the gravitational force be one-ninth of its original value?
A.
One-third of the original distance
B.
Three times the original distance
C.
Nine times the original distance
D.
One-ninth of the original distance
Correct Answer:
Three times the original distance
Explanation:
The force becomes 1/9 when the distance is multiplied by 3, because 1/3² = 1/9.
8. If the distance between two masses is decreased to one-fourth of its original value, the gravitational force becomes:
A.
One-sixteenth of the original force
B.
One-fourth of the original force
C.
Four times the original force
D.
Sixteen times the original force
Correct Answer:
Sixteen times the original force
Explanation:
For a distance r/4, the force is proportional to 1/(r/4)² = 16/r², so it becomes sixteen times larger.
9. Two objects exert a gravitational force F on each other at distance r. If their separation becomes 5r, the new force is:
A.
F/5
B.
F/10
C.
F/25
D.
25F
Correct Answer:
F/25
Explanation:
The inverse square law gives F' = F/5² = F/25 when the distance becomes 5r.
10. The gravitational force between two masses is 36 N at a certain distance. What is the force when the distance is reduced to one-third?
A.
4 N
B.
12 N
C.
108 N
D.
324 N
Correct Answer:
324 N
Explanation:
Reducing the distance to one-third increases the force by 3² = 9. Therefore, the new force is 36 × 9 = 324 N.
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