Q. A ball is tied to a string and swung in a vertical circle. At the highest point of the circle, what is the condition for the ball to remain in circular motion?
A.
Tension must be zero
B.
Tension must be maximum
C.
Weight must be zero
D.
Centripetal force must be zero
Solution
At the highest point, the tension can be zero if the centripetal force is provided entirely by the weight.
Q. A ball is tied to a string and swung in a vertical circle. At the highest point of the circle, what is the condition for the ball to just maintain circular motion?
A.
Tension = 0
B.
Tension = mg
C.
Tension > mg
D.
Tension < mg
Solution
At the highest point, the centripetal force is provided by the weight, so T + mg = mv²/r, T = 0.
Q. A ball is tied to a string and swung in a vertical circle. At the highest point, the tension in the string is 2 N and the weight of the ball is 3 N. What is the speed of the ball at the highest point if the radius of the circle is 1 m?
A.
1 m/s
B.
2 m/s
C.
3 m/s
D.
4 m/s
Solution
At the highest point, T + mg = mv²/r. 2 N + 3 N = mv²/1. v² = 5, v = √5 ≈ 2.24 m/s.
Q. A car is negotiating a curve of radius 100 m at a speed of 15 m/s. What is the minimum coefficient of friction required to prevent the car from skidding?
A.
0.15
B.
0.25
C.
0.30
D.
0.35
Solution
Frictional force = m * a_c; μmg = mv²/r; μ = v²/(rg) = (15 m/s)² / (100 m * 9.8 m/s²) ≈ 0.23.
Q. A conical pendulum consists of a mass attached to a string that swings in a horizontal circle. If the angle of the string with the vertical is θ, what is the expression for the tension in the string?
A.
mg/cos(θ)
B.
mg/sin(θ)
C.
mg/tan(θ)
D.
mg
Solution
Tension T = mg/cos(θ) to balance the vertical component of weight.
Q. A conical pendulum consists of a mass m attached to a string of length L, swinging in a horizontal circle. What is the expression for the tension in the string?
A.
T = mg
B.
T = mg/cos(θ)
C.
T = mg/sin(θ)
D.
T = m(v²/r)
Solution
In a conical pendulum, T = mg/cos(θ) where θ is the angle with the vertical.
Q. A conical pendulum swings in a horizontal circle. If the angle of the string with the vertical is θ, what is the relationship between the tension and the gravitational force acting on the pendulum bob?
A.
T = mg
B.
T = mg cos(θ)
C.
T = mg sin(θ)
D.
T = mg tan(θ)
Solution
The vertical component of tension balances the weight: T cos(θ) = mg.
Q. A conical pendulum swings in a horizontal circle. If the angle of the string with the vertical increases, what happens to the tension in the string?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
Solution
As the angle increases, the vertical component of tension must increase to balance the weight.
Q. A conical pendulum swings in a horizontal circle. If the angle of the string with the vertical is θ, what is the expression for the tension in the string?
A.
T = mg
B.
T = mg/cos(θ)
C.
T = mg/sin(θ)
D.
T = mg tan(θ)
Solution
The vertical component of tension balances the weight: T cos(θ) = mg, thus T = mg/cos(θ).
Q. A conical pendulum swings in a horizontal circle. If the angle of the string with the vertical is θ, what is the relationship between the tension in the string and the gravitational force?
A.
T = mg
B.
T = mg/cos(θ)
C.
T = mg/sin(θ)
D.
T = mg/tan(θ)
Solution
Tension T provides the centripetal force and balances the weight, T = mg/cos(θ).
Q. A conical pendulum swings in a horizontal circle. If the angle of the string with the vertical is θ, what is the relationship between the tension in the string and the gravitational force acting on the pendulum bob?
A.
T = mg
B.
T = mg cos(θ)
C.
T = mg sin(θ)
D.
T = mg tan(θ)
Solution
Tension provides the vertical component to balance the weight: T cos(θ) = mg.
Q. A conical pendulum swings with a constant speed. If the angle of the string with the vertical is θ, what is the expression for the tension in the string?
A.
mg/cos(θ)
B.
mg/sin(θ)
C.
mg/tan(θ)
D.
mg
Solution
Tension T = mg/cos(θ) to balance the vertical component of weight.
Q. A cyclist is moving in a circular track of radius 30 m with a speed of 15 m/s. What is the net force acting on the cyclist if the mass of the cyclist is 60 kg?
A.
180 N
B.
120 N
C.
90 N
D.
60 N
Solution
Centripetal force F = mv²/r = 60 kg * (15 m/s)² / 30 m = 180 N.
Q. A cyclist is moving in a circular track of radius 30 m. If the cyclist completes one round in 12 seconds, what is the angular velocity of the cyclist?
Circular motion is a crucial topic in physics that students must master for their exams. Understanding the principles of circular motion not only helps in grasping fundamental concepts but also enhances problem-solving skills. Practicing MCQs and objective questions on circular motion is essential for scoring better in school and competitive exams. By tackling these practice questions, students can identify important questions and solidify their exam preparation.
What You Will Practise Here
Definition and types of circular motion
Key formulas related to angular velocity and acceleration
Concept of centripetal force and its applications
Understanding uniform vs. non-uniform circular motion
Diagrams illustrating circular motion concepts
Real-life applications of circular motion in various fields
Important Circular Motion MCQ questions with answers
Exam Relevance
Circular motion is frequently featured in CBSE, State Boards, NEET, and JEE exams. Students can expect questions that test their understanding of concepts, calculations involving formulas, and application-based scenarios. Common question patterns include numerical problems, conceptual explanations, and diagram-based questions, making it essential to be well-prepared in this area.
Common Mistakes Students Make
Confusing linear and angular quantities
Misunderstanding the direction of centripetal force
Neglecting the role of mass in circular motion problems
Overlooking the difference between uniform and non-uniform circular motion
FAQs
Question: What is the difference between uniform and non-uniform circular motion? Answer: Uniform circular motion occurs when an object moves in a circle at a constant speed, while non-uniform circular motion involves changing speed.
Question: How do I calculate centripetal force? Answer: Centripetal force can be calculated using the formula F = mv²/r, where m is mass, v is velocity, and r is the radius of the circular path.
Start solving practice MCQs on circular motion today to test your understanding and boost your confidence for the exams. Remember, consistent practice is the key to success!
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