Circular Motion
Q. A stone is tied to a string and whirled in a horizontal circle. If the radius of the circle is doubled, what happens to the centripetal force required to maintain the circular motion at the same speed?
A.
It doubles
B.
It remains the same
C.
It halves
D.
It quadruples
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Solution
Centripetal force (F_c) = mv²/r. If r is doubled, F_c is halved for constant speed.
Correct Answer: C — It halves
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Q. A stone is tied to a string and whirled in a vertical circle of radius 1 m. What is the minimum speed at the top of the circle to keep the stone in circular motion?
A.
1 m/s
B.
2 m/s
C.
3 m/s
D.
4 m/s
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Solution
At the top, centripetal force = weight. mv²/r = mg. v² = rg. v = √(1*9.8) ≈ 3.13 m/s.
Correct Answer: B — 2 m/s
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Q. An object is moving in a circular path with a radius of 10 m and a speed of 5 m/s. What is the net force acting on the object if its mass is 2 kg?
A.
1 N
B.
2 N
C.
5 N
D.
10 N
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Solution
Centripetal force (F_c) = mv²/r = 2 kg * (5 m/s)² / (10 m) = 5 N.
Correct Answer: D — 10 N
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Q. An object is moving in a circular path with a radius of 3 m and an angular speed of 2 rad/s. What is the linear speed of the object?
A.
3 m/s
B.
6 m/s
C.
9 m/s
D.
12 m/s
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Solution
Linear speed (v) = rω = 3 m * 2 rad/s = 6 m/s.
Correct Answer: B — 6 m/s
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Q. If a body is moving in a circular path with a constant speed, which of the following statements is true?
A.
The body is in equilibrium
B.
The net force acting on the body is zero
C.
The body experiences a centripetal force
D.
The body has no acceleration
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Solution
A body moving in a circular path with constant speed experiences a centripetal force directed towards the center of the circle.
Correct Answer: C — The body experiences a centripetal force
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Q. If a body is moving in a circular path with a radius of 10 m and completes one full revolution in 5 seconds, what is its angular velocity?
A.
0.2 rad/s
B.
1.25 rad/s
C.
2 rad/s
D.
4 rad/s
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Solution
Angular velocity (ω) = 2π/T = 2π/5 = 1.25 rad/s.
Correct Answer: B — 1.25 rad/s
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Q. If a body is moving in a circular path with uniform speed, which of the following statements is true?
A.
The body has no acceleration
B.
The body has constant velocity
C.
The body experiences centripetal acceleration
D.
The body moves in a straight line
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Solution
The body experiences centripetal acceleration directed towards the center of the circle.
Correct Answer: C — The body experiences centripetal acceleration
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Q. If a body moves in a circular path with a constant speed, which of the following statements is true?
A.
The body has zero acceleration
B.
The body has constant acceleration
C.
The body has uniform velocity
D.
The body experiences centripetal acceleration
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Solution
The body experiences centripetal acceleration directed towards the center of the circle.
Correct Answer: D — The body experiences centripetal acceleration
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Q. If a stone is tied to a string and whirled in a horizontal circle of radius 2 m at a speed of 4 m/s, what is the tension in the string?
A.
2 N
B.
4 N
C.
8 N
D.
16 N
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Solution
Centripetal force (F_c) = mv²/r. Assuming mass (m) = 1 kg, F_c = 1(4²)/2 = 8 N.
Correct Answer: C — 8 N
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Q. If a stone is tied to a string and whirled in a horizontal circle of radius 2 m at a speed of 4 m/s, what is the tension in the string if the mass of the stone is 1 kg?
A.
2 N
B.
4 N
C.
8 N
D.
10 N
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Solution
Centripetal force = m(v²/r) = 1(4²/2) = 8 N. Tension in the string = 8 N.
Correct Answer: C — 8 N
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Q. If the angular velocity of a rotating object is doubled, what happens to its centripetal acceleration?
A.
It remains the same
B.
It doubles
C.
It quadruples
D.
It halves
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Solution
Centripetal acceleration (a_c) = ω²r. If ω is doubled, a_c becomes (2ω)²r = 4ω²r.
Correct Answer: C — It quadruples
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Q. If the period of a satellite in a circular orbit is T, what is the relationship between T and the radius r of the orbit?
A.
T ∝ r
B.
T ∝ r²
C.
T ∝ √r
D.
T ∝ 1/√r
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Solution
T = 2π√(r³/GM), thus T ∝ √r.
Correct Answer: C — T ∝ √r
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Q. If the speed of an object in circular motion is doubled, what happens to the centripetal acceleration?
A.
It remains the same
B.
It doubles
C.
It quadruples
D.
It halves
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Solution
Centripetal acceleration a_c = v²/r. If v is doubled, a_c increases by a factor of 4.
Correct Answer: C — It quadruples
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Q. In a conical pendulum, if the angle of the string with the vertical is increased, what happens to the horizontal component of the tension?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
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Solution
As the angle increases, the horizontal component of tension increases to provide the necessary centripetal force.
Correct Answer: A — Increases
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Q. In a uniform circular motion, which of the following quantities remains constant?
A.
Velocity
B.
Acceleration
C.
Speed
D.
Centripetal force
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Solution
In uniform circular motion, speed remains constant while velocity and acceleration change direction.
Correct Answer: C — Speed
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Q. In uniform circular motion, which of the following quantities remains constant?
A.
Speed
B.
Velocity
C.
Acceleration
D.
Centripetal force
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Solution
In uniform circular motion, the speed remains constant, but velocity and acceleration change direction.
Correct Answer: A — Speed
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Q. In uniform circular motion, which of the following statements is true?
A.
Velocity is constant
B.
Acceleration is zero
C.
Speed is constant
D.
Net force is zero
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Solution
In uniform circular motion, speed is constant but velocity changes due to direction change.
Correct Answer: C — Speed is constant
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Q. What is the angle between the velocity vector and the acceleration vector of an object moving in uniform circular motion?
A.
0°
B.
45°
C.
90°
D.
180°
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Solution
In uniform circular motion, velocity is tangential and acceleration is radial, hence the angle is 90°.
Correct Answer: C — 90°
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Q. What is the angular velocity of a wheel rotating at 300 revolutions per minute?
A.
10π rad/s
B.
20π rad/s
C.
30π rad/s
D.
40π rad/s
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Solution
Angular velocity (ω) = 2π * (300/60) = 10π rad/s.
Correct Answer: B — 20π rad/s
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Q. What is the angular velocity of a wheel that makes 10 revolutions in 5 seconds?
A.
2π rad/s
B.
4π rad/s
C.
10π rad/s
D.
20π rad/s
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Solution
Angular velocity ω = θ/t = (10 * 2π rad) / 5 s = 4π rad/s.
Correct Answer: B — 4π rad/s
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Q. What is the relationship between the angular velocity (ω) and the linear velocity (v) in circular motion?
A.
v = ωr
B.
v = r/ω
C.
v = ω²r
D.
v = r²ω
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Solution
The relationship is given by v = ωr, where r is the radius of the circular path.
Correct Answer: A — v = ωr
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Q. What is the relationship between the angular velocity and linear velocity of an object moving in a circular path?
A.
v = ωr
B.
v = r/ω
C.
v = ω/r
D.
v = ω²r
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Solution
Linear velocity (v) is related to angular velocity (ω) by the formula v = ωr.
Correct Answer: A — v = ωr
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Q. What is the relationship between the angular velocity and linear velocity of an object in circular motion?
A.
v = ωr
B.
v = r/ω
C.
v = ω/r
D.
v = ω²r
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Solution
Linear velocity (v) is related to angular velocity (ω) by the equation v = ωr.
Correct Answer: A — v = ωr
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