Physics Practice Test: Circular Motion and Gravitation
- Circular Motion and Gravitation
- 10 questions
- 15 minutes
These 10 questions cover uniform circular motion and Newton's law of universal gravitation. Use g = 9.8 m/s² near Earth's surface. Remember that centripetal force is not a new kind of force: it is the net inward force supplied by tension, friction, gravity or a normal force.
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Question 1
A car drives around a curve of radius 50 m at a constant 15 m/s. What is its centripetal acceleration?
Correct answer: C
ac = v²/r = 225/50 = 4.5 m/s². 0.30 m/s² uses v/r without squaring the speed.
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Question 2
Astronauts in an orbiting space station float inside the cabin. What is the best explanation?
Correct answer: D
At typical station heights gravity is still about 90% as strong as at the surface. The astronauts float because they and the station fall around Earth at the same rate, so nothing presses against them.
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Question 3
A ball is swung in a horizontal circle on a string. At one moment the string breaks. Seen from above, how does the ball move right after that?
Correct answer: A
Without the string there is no inward force, so the ball keeps the velocity it had, which points along the tangent. Moving straight outward would need an outward force that does not exist.
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Question 4
A stone on a 2.0 m rope is whirled in a circle and completes one revolution every 0.50 s. What is its speed?
Correct answer: B
v = 2πr/T = 2π(2.0)/0.50 ≈ 25 m/s. 4.0 m/s divides the radius by the period and forgets that one lap is 2πr long.
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Question 5
A car rounds a flat curve of radius 40 m. The coefficient of static friction between tires and road is 0.50. What is the highest speed it can have without skidding?
Correct answer: A
Friction provides the centripetal force: μmg = mv²/r, so v = √(0.50 × 9.8 × 40) = 14 m/s. 20 m/s ignores the coefficient of friction.
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Question 6
A roller coaster goes around a vertical loop with a radius of 2.5 m. What is the minimum speed at the top of the loop for the car to stay on the track?
Correct answer: D
At the minimum speed, gravity alone supplies the centripetal force: mg = mv²/r, so v = √(gr) = √24.5 ≈ 4.9 m/s. 7.0 m/s is √(2gr), and 24.5 is gr without the square root.
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Question 7
Two objects attract each other with a gravitational force F. If the mass of each object is doubled and the distance between them stays the same, what is the new force?
Correct answer: C
F = Gm1m2/r², so doubling both masses multiplies the product by 2 × 2 = 4. 2F would be the answer if only one mass doubled.
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Question 8
An astronaut weighs 800 N on Earth's surface. What would the gravitational force on her be at a height of one Earth radius above the surface?
Correct answer: B
At one radius above the surface she is 2 radii from Earth's center, so the force is 1/2² = 1/4 as large: 800/4 = 200 N. 400 N treats the force as inversely proportional to distance instead of distance squared.
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Question 9
A planet has twice the mass of Earth and twice Earth's radius. What is the acceleration due to gravity at its surface?
Correct answer: A
g = GM/R², so the factors give 2/2² = 1/2, and g = 9.8/2 = 4.9 m/s². 9.8 m/s² assumes the two changes cancel, but the radius counts twice.
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Question 10
Satellite B orbits a planet at 4 times the orbital radius of satellite A. Both orbits are circular. How does B's orbital period compare with A's?
Correct answer: C
Kepler's third law says T² ∝ r³, so T ∝ r3/2 = 43/2 = 8. 16 would come from T ∝ r².
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