Q. A cyclist is negotiating a circular track of radius 30 m. If the cyclist's speed is 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_c = mv²/r = 60 kg * (15 m/s)² / 30 m = 180 N.
Q. A cyclist is negotiating a circular track of radius 30 m. If the cyclist's speed is 15 m/s, what is the net force acting on the cyclist towards the center of the track?
A.
50 N
B.
75 N
C.
100 N
D.
125 N
Solution
Centripetal force (F_c) = mv²/r. Assuming mass m = 100 kg, F_c = (100 kg)(15 m/s)² / (30 m) = 75 N.
Q. A cyclist is negotiating a circular turn of radius 30 m at a speed of 15 m/s. What is the minimum coefficient of friction required to prevent slipping?
A.
0.25
B.
0.5
C.
0.75
D.
1
Solution
Frictional force = m * a_c; μmg = mv²/r; μ = v²/(rg) = (15²)/(30*9.8) = 0.25.
Q. A mass m is attached to a string and is whirled in a horizontal circle. If the radius of the circle is halved, what happens to the tension in the string if the speed remains constant?
A.
It doubles
B.
It remains the same
C.
It halves
D.
It quadruples
Solution
Tension T = mv²/r. If r is halved, T doubles for constant speed.
Q. A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, what is the condition for the mass to just complete the circular motion?
A.
Tension = 0
B.
Tension = mg
C.
Tension = 2mg
D.
Tension = mg/2
Solution
At the highest point, the centripetal force is provided by the weight of the mass, so T + mg = mv²/r. For T = 0, mg = mv²/r.
Q. A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, what is the minimum speed required to keep the mass in circular motion?
A.
√(g*r)
B.
g*r
C.
2g*r
D.
g/2
Solution
At the highest point, the centripetal force is provided by the weight. Minimum speed = √(g*r).
Q. A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, the tension in the string is T. What is the expression for T?
A.
T = mg
B.
T = mg - mv²/r
C.
T = mg + mv²/r
D.
T = mv²/r
Solution
At the highest point, T + mg = mv²/r, thus T = mg - mv²/r.
Q. A mass m is attached to a string and is whirled in a vertical circle. At the top of the circle, the tension in the string is T. What is the expression for the tension at the bottom of the circle?
Q. A mass m is attached to a string of length L and is swung in a vertical circle. At the highest point of the circle, what is the minimum speed required to keep the mass in circular motion?
A.
√(gL)
B.
√(2gL)
C.
gL
D.
2gL
Solution
At the highest point, the centripetal force must equal the weight: mv²/L = mg, thus v = √(gL).
Q. A particle moves in a circular path of radius r with a constant angular acceleration α. What is the expression for the angular displacement θ after time t?
A.
θ = αt²
B.
θ = 0.5αt²
C.
θ = αt
D.
θ = 0.5αt
Solution
Angular displacement θ = 0.5αt² for constant angular acceleration.
Q. A satellite is in a circular orbit around the Earth. If the radius of the orbit is doubled, what happens to the gravitational force acting on the satellite?
A.
It doubles
B.
It halves
C.
It becomes four times
D.
It becomes one-fourth
Solution
Gravitational force ∝ 1/r². If radius is doubled, force becomes 1/(2²) = 1/4.
Q. A satellite is in a circular orbit around the Earth. If the radius of the orbit is 7000 km and the gravitational acceleration is 9.8 m/s², what is the speed of the satellite?
Q. A satellite is in a circular orbit around the Earth. If the radius of the orbit is 7000 km and the speed of the satellite is 7.9 km/s, what is the centripetal acceleration?
Q. A stone is tied to a string and swung in a vertical circle. At the highest point, the tension in the string is 5 N and the weight of the stone is 10 N. What is the speed of the stone at the highest point if the radius of the circle is 2 m?
A.
2 m/s
B.
3 m/s
C.
4 m/s
D.
5 m/s
Solution
At the highest point, T + mg = mv²/r. 5 + 10 = (m*v²)/2. Solving gives v = 4 m/s.
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 stone's circular motion at the same speed?
A.
It doubles
B.
It remains the same
C.
It halves
D.
It quadruples
Solution
Centripetal force (F_c) = mv²/r. If r is doubled, F_c is halved for constant speed.
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
Solution
Centripetal force (F_c) = mv²/r. If r is doubled, F_c is halved for constant speed.
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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