physics : class11 Torque Definition : Moment of a Force : Motion of System of Particles and Rigid Body MCQ Questions and Answers
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Torque Definition
MCQ questions and answers.
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MCQ Questions
1. A force vector is given by F = (3i - 4j) N and its point of application has position vector r = (2i + j) m relative to the origin. What is the torque of the force about the origin?
A.
11k N m
B.
-11k N m
C.
5k N m
D.
-5k N m
Correct Answer:
-11k N m
Explanation:
Torque is defined as τ = r × F. Thus, τ = (2i + j) × (3i - 4j) = [2(-4) - 1(3)]k = -11k N m.
2. A force of magnitude 20 N acts at a point whose position vector from the origin has magnitude 0.50 m. If the torque about the origin is 6 N m, what is the angle between the position vector and the force?
A.
30°
B.
37°
C.
53°
D.
90°
Correct Answer:
37°
Explanation:
The magnitude of torque is τ = rF sinθ. Therefore, sinθ = 6/(0.50 × 20) = 0.6, giving θ ≈ 37° for the acute angle.
3. A force acts along a line whose perpendicular distance from a chosen origin is 0.25 m. If the magnitude of the force is 80 N, what is the magnitude of its torque about that origin?
A.
20 N m
B.
32 N m
C.
80 N m
D.
320 N m
Correct Answer:
20 N m
Explanation:
For a force, torque magnitude can be written as τ = Fd, where d is the perpendicular distance from the origin to the force's line of action. Hence τ = 80 × 0.25 = 20 N m.
4. Which statement most precisely represents the vector definition of torque of a force about a point?
A.
Torque equals the scalar product of force and position vector
B.
Torque equals the vector product of position vector and force
C.
Torque equals force divided by position vector
D.
Torque equals the product of force and the distance to its point of application
Correct Answer:
Torque equals the vector product of position vector and force
Explanation:
The torque of a force about a point is defined by τ = r × F, where r is drawn from the reference point to the point of application of the force.
5. A force F = 4i + 2j N is applied at position r = 3i - j m relative to the origin. Which is the correct torque about the origin?
A.
10k N m
B.
-10k N m
C.
14k N m
D.
-14k N m
Correct Answer:
10k N m
Explanation:
Using τ = r × F, τ = (3i - j) × (4i + 2j) = [3(2) - (-1)(4)]k = 10k N m.
6. For a fixed force vector applied at a fixed point, the torque about an origin is zero. Which condition must necessarily hold?
A.
The force must be perpendicular to the position vector
B.
The force must have the same magnitude as the position vector
C.
The force's line of action must pass through the origin
D.
The position vector must be parallel to the torque vector
Correct Answer:
The force's line of action must pass through the origin
Explanation:
Since |τ| = Fd, zero torque for a nonzero force requires the perpendicular distance d from the origin to the force's line of action to be zero. Thus, the line of action passes through the origin.
7. A force F = 5i N acts at position r = 2j m relative to the origin. What is the direction of the torque about the origin?
A.
Along the positive x-axis
B.
Along the positive y-axis
C.
Along the positive z-axis
D.
Along the negative z-axis
Correct Answer:
Along the negative z-axis
Explanation:
The torque is τ = r × F = 2j × 5i = 10(j × i) = -10k N m, so its direction is along the negative z-axis.
8. A force is decomposed into components parallel and perpendicular to the position vector from the reference point. Which component determines the torque magnitude?
A.
Only the component parallel to the position vector
B.
Only the component perpendicular to the position vector
C.
The algebraic sum of both components without regard to direction
D.
The component parallel to the position vector multiplied by the position magnitude
Correct Answer:
Only the component perpendicular to the position vector
Explanation:
Torque magnitude is τ = rF sinθ = rF_perpendicular. The parallel component has zero moment arm and contributes no torque.
9. A force of magnitude 50 N acts at an angle of 150° to a position vector of magnitude 0.40 m. What is the magnitude of the torque?
A.
10 N m
B.
17.3 N m
C.
20 N m
D.
25 N m
Correct Answer:
10 N m
Explanation:
Using τ = rF sinθ, τ = 0.40 × 50 × sin150° = 20 × 0.5 = 10 N m. The obtuse angle gives the same magnitude as its supplementary acute angle.
10. The torque of a force about a point is an axial vector. If the force and its position vector both lie in the xy-plane, which direction can the torque have?
A.
Only within the xy-plane
B.
Only along the positive z-axis, regardless of orientation
C.
Only along the negative z-axis, regardless of orientation
D.
Along the z-axis, with its sign determined by the sense of rotation
Correct Answer:
Along the z-axis, with its sign determined by the sense of rotation
Explanation:
The cross product r × F is perpendicular to the plane containing r and F. For vectors in the xy-plane, torque is along the z-axis, with positive or negative direction fixed by the right-hand rule.
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