Q. If a rigid body rotates about a fixed axis, which of the following quantities remains constant?
A.
Angular velocity
B.
Angular acceleration
C.
Moment of inertia
D.
Torque
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Solution
If no external torques act on the body, the angular velocity can remain constant during rotation.
Correct Answer:
A
— Angular velocity
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Q. In a system of rigid bodies, if one body exerts a force on another, what is true about the reaction force?
A.
It is equal and opposite
B.
It is greater than the applied force
C.
It is less than the applied force
D.
It acts in the same direction
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Solution
According to Newton's third law, for every action, there is an equal and opposite reaction, meaning the reaction force is equal and opposite to the applied force.
Correct Answer:
A
— It is equal and opposite
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Q. In rotational dynamics, what does the moment of inertia depend on?
A.
Mass and shape of the object
B.
Only the mass of the object
C.
Only the shape of the object
D.
Mass and velocity of the object
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Solution
The moment of inertia depends on both the mass distribution and the shape of the object relative to the axis of rotation.
Correct Answer:
A
— Mass and shape of the object
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Q. What happens to the angular momentum of a rigid body if no external torque acts on it?
A.
It increases
B.
It decreases
C.
It remains constant
D.
It becomes zero
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Solution
According to the law of conservation of angular momentum, if no external torque acts on a rigid body, its angular momentum remains constant.
Correct Answer:
C
— It remains constant
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Q. What is the gravitational force between two masses?
A.
F = G(m1m2)/r^2
B.
F = G(m1 + m2)/r^2
C.
F = G(m1 - m2)/r^2
D.
F = G(m1m2)r^2
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Solution
The gravitational force between two masses is given by Newton's law of gravitation: F = G(m1m2)/r^2.
Correct Answer:
A
— F = G(m1m2)/r^2
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Q. What is the kinetic energy of a rotating rigid body?
A.
KE = 1/2 Iω^2
B.
KE = Iω
C.
KE = 1/2 mv^2
D.
KE = mvω
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Solution
The kinetic energy of a rotating rigid body is given by KE = 1/2 Iω^2, where I is the moment of inertia and ω is the angular velocity.
Correct Answer:
A
— KE = 1/2 Iω^2
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Q. What is the moment of inertia for a solid cylinder about its central axis?
A.
1/2 m r^2
B.
m r^2
C.
1/3 m r^2
D.
m r
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Solution
The moment of inertia for 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 net force acting on a rigid body in equilibrium?
A.
Zero
B.
Equal to its weight
C.
Equal to its mass times acceleration
D.
Equal to the applied force
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Solution
In equilibrium, the net force acting on a rigid body is zero, meaning all forces balance out.
Correct Answer:
A
— Zero
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Q. What is the relationship between linear velocity and angular velocity for a point on a rotating rigid body?
A.
v = rω
B.
v = ω/r
C.
v = r/ω
D.
v = ω + r
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Solution
The relationship between linear velocity (v) and angular velocity (ω) for a point on a rotating rigid body is given by v = rω, where r is the radius.
Correct Answer:
A
— v = rω
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Q. What is the relationship between torque and angular acceleration for a rigid body?
A.
Torque = Moment of inertia × Angular velocity
B.
Torque = Moment of inertia × Angular acceleration
C.
Torque = Angular acceleration / Moment of inertia
D.
Torque = Angular velocity × Moment of inertia
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Solution
The relationship is given by the equation τ = Iα, where τ is torque, I is moment of inertia, and α is angular acceleration.
Correct Answer:
B
— Torque = Moment of inertia × Angular acceleration
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Q. What is the torque produced by a force applied at a distance?
A.
τ = rF sin(θ)
B.
τ = rF cos(θ)
C.
τ = F/r
D.
τ = F + r
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Solution
The torque produced by a force applied at a distance from the pivot point is given by τ = rF sin(θ), where θ is the angle between the force and the lever arm.
Correct Answer:
A
— τ = rF sin(θ)
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Q. What is the work done by a constant force on a rigid body moving in the direction of the force?
A.
Force × Distance
B.
Force × Distance × cos(θ)
C.
Force × Distance × sin(θ)
D.
Force / Distance
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Solution
The work done is calculated as W = Fd cos(θ), where θ is the angle between the force and the direction of motion.
Correct Answer:
B
— Force × Distance × cos(θ)
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Q. What is the work done by a constant force?
A.
W = Fd cos(θ)
B.
W = Fd sin(θ)
C.
W = F + d
D.
W = F/d
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Solution
The work done by a constant force is calculated using the formula W = Fd cos(θ), where θ is the angle between the force and the direction of motion.
Correct Answer:
A
— W = Fd cos(θ)
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Q. Which of the following is a correct expression for kinetic energy of a rotating rigid body?
A.
KE = 1/2 mv^2
B.
KE = 1/2 Iω^2
C.
KE = Iα
D.
KE = 1/2 mω^2
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Solution
The kinetic energy of a rotating rigid body is given by KE = 1/2 Iω^2, where I is the moment of inertia and ω is the angular velocity.
Correct Answer:
B
— KE = 1/2 Iω^2
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Q. Which of the following statements is true regarding the conservation of momentum in a rigid body system?
A.
Momentum is conserved only in elastic collisions
B.
Momentum is conserved in all types of collisions
C.
Momentum is not conserved in inelastic collisions
D.
Momentum is conserved only in isolated systems
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Solution
Momentum is conserved in isolated systems, regardless of the type of collision.
Correct Answer:
D
— Momentum is conserved only in isolated systems
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