Q. If a rolling object has a radius of 0.5 m and rolls with a linear speed of 2 m/s, what is its angular speed?
A.
4 rad/s
B.
2 rad/s
C.
1 rad/s
D.
3 rad/s
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Solution
The angular speed (ω) can be calculated using the formula ω = v/r. Here, ω = 2 m/s / 0.5 m = 4 rad/s.
Correct Answer:
A
— 4 rad/s
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Q. If a rolling object has a translational speed of v and a radius r, what is its angular speed?
A.
v/r
B.
rv
C.
v^2/r
D.
r/v
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Solution
The angular speed (ω) of a rolling object is related to its translational speed (v) by the equation ω = v/r.
Correct Answer:
A
— v/r
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Q. If a solid sphere and a hollow sphere of the same mass and radius roll down an incline, which will reach the bottom first?
A.
Solid sphere
B.
Hollow sphere
C.
Both will reach at the same time
D.
It depends on the angle of the incline
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Solution
The solid sphere has a lower moment of inertia compared to the hollow sphere, allowing it to accelerate faster down the incline.
Correct Answer:
A
— Solid sphere
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Q. In a stable rolling motion, what is the relationship between the center of mass and the base of the object?
A.
The center of mass must be above the base.
B.
The center of mass must be below the base.
C.
The center of mass must be at the edge of the base.
D.
The center of mass can be anywhere.
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Solution
For stability in rolling motion, the center of mass must be above the base to ensure that the object does not tip over.
Correct Answer:
A
— The center of mass must be above the base.
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Q. In terms of stability, what is the effect of lowering the center of mass of a rolling object?
A.
Increases stability
B.
Decreases stability
C.
No effect on stability
D.
Depends on the object's shape
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Solution
Lowering the center of mass of a rolling object increases its stability, making it less likely to tip over.
Correct Answer:
A
— Increases stability
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Q. What happens to the total mechanical energy of a rolling object if it rolls without slipping?
A.
It increases
B.
It decreases
C.
It remains constant
D.
It depends on the surface
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Solution
In rolling without slipping, the total mechanical energy (potential + kinetic) remains constant due to conservation of energy.
Correct Answer:
C
— It remains constant
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Q. What is the condition for a rolling object to be in pure rolling motion?
A.
The object must not slide at all.
B.
The object must have a constant velocity.
C.
The object must have a constant acceleration.
D.
The object must be on a flat surface.
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Solution
Pure rolling motion occurs when the point of contact between the rolling object and the surface is at rest relative to the surface, meaning there is no sliding.
Correct Answer:
A
— The object must not slide at all.
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Q. What is the effect of increasing the radius of a rolling object on its moment of inertia?
A.
It decreases the moment of inertia.
B.
It increases the moment of inertia.
C.
It has no effect on the moment of inertia.
D.
It depends on the mass of the object.
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Solution
The moment of inertia increases with the square of the radius, as seen in the formula I = k m r^2, where k is a constant depending on the shape.
Correct Answer:
B
— It increases the moment of inertia.
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Q. What is the moment of inertia of a solid cylinder about its central axis?
A.
1/2 m r^2
B.
1/3 m r^2
C.
m r^2
D.
m r^2 / 2
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Solution
The moment of inertia of a solid cylinder about its central axis is given by I = 1/2 m r^2.
Correct Answer:
A
— 1/2 m r^2
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Q. What is the primary force acting on a rolling object on an incline?
A.
Friction
B.
Normal force
C.
Gravitational force
D.
Centripetal force
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Solution
The primary force acting on a rolling object on an incline is gravitational force, which causes it to roll down the incline.
Correct Answer:
C
— Gravitational force
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Q. What is the relationship between linear momentum and angular momentum for a rolling object?
A.
They are equal.
B.
Angular momentum is linear momentum multiplied by radius.
C.
Angular momentum is linear momentum divided by radius.
D.
They are independent of each other.
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Solution
The angular momentum (L) of a rolling object is related to its linear momentum (p) by the equation L = p * r, where r is the radius.
Correct Answer:
B
— Angular momentum is linear momentum multiplied by radius.
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Q. What type of energy is associated with a rolling object due to its motion?
A.
Kinetic energy
B.
Potential energy
C.
Thermal energy
D.
Elastic energy
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Solution
A rolling object possesses kinetic energy due to both its translational and rotational motion.
Correct Answer:
A
— Kinetic energy
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Q. Which of the following factors does NOT affect the stability of a rolling object?
A.
Height of the center of mass
B.
Base width of the object
C.
Mass of the object
D.
Speed of the object
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Solution
The speed of the object does not directly affect its stability; stability is influenced by the height of the center of mass and the base width.
Correct Answer:
D
— Speed of the object
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Q. Which of the following is true about the rolling motion of a wheel on a flat surface?
A.
The friction is zero.
B.
The friction is static.
C.
The friction is kinetic.
D.
The wheel does not experience any forces.
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Solution
When a wheel rolls without slipping, the friction involved is static friction, which prevents sliding between the wheel and the surface.
Correct Answer:
B
— The friction is static.
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Q. Which of the following is true about the rolling motion of a wheel?
A.
The linear velocity is equal to the angular velocity times the radius.
B.
The linear velocity is half of the angular velocity times the radius.
C.
The angular velocity is equal to the linear velocity divided by the radius.
D.
The linear velocity is independent of the radius.
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Solution
The relationship between linear velocity (v) and angular velocity (ω) is given by v = ωr, which can be rearranged to ω = v/r.
Correct Answer:
C
— The angular velocity is equal to the linear velocity divided by the radius.
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