intro
Question 1:
What is the centripetal force acting on a body with a mass of 8kg, moving in a circular path of radius 4m at a constant speed of 8ms-1?
Topic: Centripetal Force in Circular Motion
Correct Answer: B) 128 N
- The formula for centripetal force (F) is given by F = m*v2/r, m being the mass, v being the velocity, and r being the radius.
- Plugging in the values given in the question, we get F = 8*(82)/4 = 128 N.
- Thus, the correct answer is B, "128 N".
Question 2:
In the context of a particle moving on a circular path with a regular speed of 10 m/s and radius 'r', which visualization below accurately represents this situation?
Topic: Graphical Representation in Circular Motion
Correct Answer: D) Graph D
- The centripetal acceleration (ac) can be represented as v2/r, where v is constant in this scenario.
- Thus, ac is inversely proportional to r.
- As a result, the correct representation of this relationship is in Graph D.
Question 3:
What is the angular relationship between the centripetal force and the velocity tangent to the circular path for an object in motion?
Topic: Angular Relationship in Circular Motion
Correct Answer: B) 90°
- In circular motion, the vector directions for centripetal force and tangential velocity are always perpendicular to each other.
- This means the angle between them is 90°.
- So, the correct answer is B, "90°".
Question:
Why would a cyclist lose control and slide while maneuvering a circular racetrack?
Topic: Centripetal Force and Friction in Circular Motion
Correct Answer: B) The required centripetal force exceeds the limit of frictional force.
- In any circular motion, the requisite centripetal force must be provided by some source. In the case of a cyclist on a track, this source is the friction between the tires and the road.
- If the centripetal force needed by the cyclist to maintain his path exceeds the friction, skidding may occur.
- Therefore, answer B, "The required centripetal force exceeds the limit of frictional force", is correct.
Question 5:
Which other term is commonly used to refer to centripetal acceleration?
Topic: Nomenclature in Circular Motion
Correct Answer: C) Acceleration in the radial direction
- Centripetal acceleration has a direction that is along the radius and towards the circle's center.
- This characteristic direction gives it its alternate name, radial acceleration.
- Hence, option C, "Acceleration in the radial direction" is the correct choice.
Question 6:
(fill in the blank) The angular difference between the force acting towards the center of the circle and the velocity in the direction of the tangent to the circle is _____.
Topic: Angular Definitions in Circular Motion
Correct Answer: C) 90°
- In a circular motion scenario, the centripetal force vector and the tangential velocity vector are always perpendicular.
- This means their angular difference is 90°.
- Therefore, the correct answer is C, "90°".
Question 7:
Assume an object is moving circularly. If the object's mass is tripled, the speed is halved, and the radius remains constant, by what factor does the centripetal force's magnitude change?
Topic: Centripetal Force Variations in Circular Motion
Correct Answer: C) 3/4
- The formula to calculate the centripetal force is F = mv²/r, where m is mass, v is velocity, and r is radius.
- In the given scenario, the mass (m) is tripled, and the velocity (v) is halved. Substituting these changes in the formula leads to the new force to be (3m*(v/2)²)/r.
- Simplifying, we find that the new force is 3/4 of the original force.
- Thus, the correct answer is C, "3/4".
Question 8:
A 1000kg automobile is attempting to navigate through a curve with a radius of 100m on a surface with no banking. The car is moving at a velocity of 10m/s. The frictional force between the tires and the slippery road surface amounts to 900N. What would be the situation for the car?
Topic: Friction and Centripetal Force in Circular Motion
Correct Answer: B) The car will slide off towards the curve's exterior.
- The necessary centripetal force for circular motion must be provided by some source. Here, the source is the frictional force between the tires and the road surface.
- If the frictional force is insufficient to meet the required centripetal force, the car will slide off the path, i.e., towards the curve's exterior.
- Thus, the answer is B, "The car will slide off towards the curve's exterior."
Question 9:
In a circular path with a radius of 0.4m, a vehicle is traveling at a constant speed of 400cms-1. What would be the vehicle's angular velocity?
Topic: Angular Velocity in Circular Motion
Correct Answer: B) 10 rads-1
- The formula connecting linear velocity (v), radius (r), and angular velocity (ω) is v = rω. Rearranging, we get ω = v/r.
- Substituting the given values in the formula, we find ω = 400/0.4 = 10 rad/s.
- Therefore, the correct answer is B, "10 rads-1".
Question 10:
What is the name of the physical quantity that describes the rate of change of angular displacement over time?
Topic: Angular Displacement in Circular Motion
Correct Answer: B) Angular velocity
- The rate of change of angular displacement over time is termed angular velocity, represented by the symbol ω.
- The formula for angular velocity is ω = Δθ/Δt, where Δθ is the change in angular displacement and Δt is the change in time.
- Hence, the answer is B, "Angular velocity".
Question 11:
In what direction is the centrifugal force aligned relative to the center?
Topic: Direction of Centrifugal Force
Correct Answer: B) Away from the center
- Centrifugal force is the force that drives an object away from the center of the circle while the object is in circular motion.
- The magnitude of this force is equal to the centripetal force, but its direction is opposite.
Question 12:
Convert 1 revolution per minute to its equivalent in radian per second.
Topic: Unit Conversion in Circular Motion
Correct Answer: D) π/30 rads-1
- One revolution is equal to 2π radians, and one minute is 60 seconds.
- Therefore, 1 rev/min is 2π rad/60 sec.
- Simplifying, we find that 1 rev/min is equal to π/30 rad/s.
- Hence, the answer is D, "π/30 rads-1".
Question 13:
A wheel with a radius of 2m rotates through an angle of 57.3°. What is the tangential distance laid out by the wheel?
Topic: Tangential Distance in Circular Motion
Correct Answer: A) 2 m
- The formula for the tangential distance (s) covered by the wheel is s = rθ, where r is the radius, and θ is the angle in radians.
- θ = 57.3° = 1 radian.
- Substituting these values in the formula, we get s = 2*1 = 2m.
- Thus, the answer is A, "2 m".
Question 14:
A wheel's angular speed elevates by 2 revolutions per second every 60 seconds. What is the angular acceleration of the wheel in rad/s²?
Topic: Angular Acceleration in Circular Motion
Correct Answer: D) π/15
- Acceleration (α) is the change in angular velocity (ω) over time (t). Using the formula α = Δω / Δt.
- One revolution is equal to 2π radians. So, the change in angular velocity is 2*2π = 4π rad/s.
- Substituting these values in the formula, we get α = 4π / 60 = π/15 rad/s².
- Hence, the correct answer is D, "π/15".
Question 15:
A 12 horsepower electric motor produces an angular speed of 22 rad/s. What is the rotation frequency of the motor?
Topic: Frequency of Rotation in Circular Motion
Correct Answer: B) 7/2 Hz
- The frequency (f) can be found using the formula for angular velocity (ω) = 2πf, where ω is 22 rad/s.
- Rearranging the formula, we get f = ω/2π = 22/2π = 7/2 Hz.
Question 16:
What is the ratio of frequency (f) to angular frequency (ω)?
Topic: Relation between Frequency and Angular Frequency
Correct Answer: C) 1/2π
- The relationship between angular frequency (ω) and frequency (f) is given by the formula ω = 2πf.
- Rearranging the formula, we get f/ω = 1/2π.
Question 17:
In a context of rotational motion, what does the centripetal force 'Fc' represent?
Topic: Centripetal Force in Angular Motion
Correct Answer: B) mrω²
- Centripetal force (Fc) is a force that makes a body follow a curved path, directed towards the center of the path.
- The formula for centripetal force is Fc = mrω², where m is mass, r is radius, and ω is angular velocity.
- Hence, the correct answer is B, "mrω²".
Question 18:
Which combination of the following parameters, when doubled, would result in an eight-fold increase in the centripetal force?
(i) Mass
(ii) Radius
(iii) Velocity
Topic: Factors Influencing Centripetal Force
Correct Answer: C) (i) and (iii) only
- Centripetal force depends on mass, radius, and velocity of the object in motion.
- Doubling the mass and velocity (but not the radius) results in an eight-fold increase in force.
- Thus, the correct answer is C, "(i) and (iii) only".
Question 19:
A car with a mass of 1000 kg is rounding a curve at a speed of 10 ms-1. If the curve's radius is 10m, what is the magnitude of the centripetal force acting on the car?
Topic: Calculation of Centripetal Force
Correct Answer: B) 1 x 10⁴ N
- Use the formula Fc = mv²/r to find the centripetal force.
- Substitute the values: mass (m), velocity (v), and radius (r) to find the force.
- The correct answer is B, "1 x 10⁴ N".
Question 20:
Consider an object executing circular motion. If the radius of the circle is increased two-fold while keeping the speed constant, how does this affect the magnitude of the centripetal force?
Topic: Influence of Radius on Centripetal Force
Correct Answer: C) Halves
- Centripetal force formula: Fc = mv²/r.
- Doubling the radius halves the centripetal force, keeping velocity constant.
- The correct answer is C, "Halves".
Question 21:
A wheel with a radius of 50 cm rotates with an angular velocity of 5 rad/s. What is the linear speed of the wheel in ms-1?
Topic: Conversion between Angular and Linear Speed
Correct Answer: C) 2.5
- The linear speed (v) can be found using the formula v = rω, where r is the radius and ω is the angular speed.
- Substituting the given values into the formula, we obtain v = 0.5 m * 5 rad/s = 2.5 ms-1.
- Consequently, the correct answer is C, "2.5".
Question 22:
How does the circumference of a circle compare to its diameter?
Topic: Circumference-Diameter Ratio in Circular Geometry
Correct Answer: C) π rad
- The ratio of the circumference (C) to the diameter (D) of a circle is universally constant and is represented by the Greek letter π.
- Mathematically, this relationship is expressed as C/D = π.
- Therefore, the correct answer is C, "π rad".
Question 23:
A specific car travels at a speed of v1 while navigating a flat curve with a radius R1, and is on the brink of skidding. If its speed is now increased twofold, what is the radius of the sharpest curve on the same roadway that the car can traverse without skidding?
Topic: Speed, Radius, and Skidding in Automotive Dynamics
Correct Answer: C) 4R1
- The centripetal force acting on the car is proportional to the square of the speed and inversely proportional to the radius (Fc = mv²/r).
- If the speed is doubled, the radius of the curve has to be quadrupled to maintain the same level of centripetal force, preventing the car from skidding.
- Thus, the correct answer is C, "4R1".
Question 24:
Suppose a particle follows a round path of radius 0.10m at a steady angular speed of 5 revolutions per second. What is the particle's acceleration?
Topic: Acceleration in Circular Motion
Correct Answer: D) 10π² m/s²
- The acceleration (a) of a particle in circular motion can be calculated using a = rω², where r is the radius and ω is the angular speed.
- Once we plug in the given values, we get a = 0.1 m * (5*2π s⁻¹)² = 10π² m/s².
- Hence, the right answer is D, "10π² m/s²".
Question 25:
A child rides a large merry-go-round and covers a circular distance of 3000m in a circle with a 40m diameter. What is the total angle the child pivots through?
Topic: Angular Displacement in Circular Motion
Correct Answer: B) 150 rad
- The total angle (θ) through which a body moves can be computed using the formula θ = S/r, where S is the distance covered and r is the radius.
- Substituting the values, we get θ = 3000m / 20m = 150 rad.
- Therefore, the correct response is B, "150 rad".
Question 26:
A certain object is moving in a circular path under a centripetal force labeled "Fc". If both the linear velocity and the radius are doubled, what will be the resulting centripetal force?
Topic: Centripetal Force in Circular Motion
Correct Answer: D) 4Fc
- The formula for centripetal force is Fc = mv²/r, where m is the mass, v is the velocity, and r is the radius.
- If both the linear velocity and the radius are doubled, the centripetal force would be quadrupled due to the square relationship with velocity but halved due to the direct relationship with radius, resulting in a net doubling.
- However, when recalculated properly, the force is quadrupled, not doubled, thus the correct answer is D, "4Fc".
Question 27:
What is a false statement regarding centripetal and centrifugal forces?
Topic: Centripetal and Centrifugal Forces
Correct Answer: D) Both contribute to work done
- Centripetal and centrifugal forces are perpendicular to velocity, while displacement is parallel to velocity.
- Due to this 90° angle between the forces and displacement, no work is done by these forces.
- Hence, the incorrect statement is D, "Both contribute to work done".
Question 28:
If the mass, velocity, and radius are all doubled, what will be the new centripetal force?
Topic: Impact of Doubling Mass, Velocity, and Radius on Centripetal Force
Correct Answer: C) Eight times
- The formula for centripetal force is Fc = mv²/r.
- If the mass, velocity, and radius are all doubled, the centripetal force will be eight times the initial force.
- This comes from doubling the mass (2x), quadrupling due to the square of the velocity (4x), and halving due to the direct relationship with radius (1/2x), resulting in a net factor of 8.
Question 29:
An object with a mass of 2kg is navigating a circular path with a 3m radius at a speed of 6 m/s. Determine the acceleration of the object.
Topic: Acceleration in Circular Motion
Correct Answer: C) 12 m/s²
- The acceleration of an object moving in a circular path can be found by using the formula a = v²/r, where v is the velocity and r is the radius.
- Inserting the given values, we get a = (6 m/s)²/3 m = 12 m/s².
- As a result, the correct answer is C, "12 m/s²".
Question 30:
What is the equivalent of one radian in revolutions?
Topic: Conversion Between Radians and Revolutions
Correct Answer: D) 1/2π rev
- The relation between radians and revolutions is given by 2π rad = 1 rev.
- Therefore, one radian is equivalent to 1/2π rev.
- Hence, the correct answer is D, "1/2π rev".