physics : class11 Reference Point Dependence : Moment of a Force : Motion of System of Particles and Rigid Body MCQ Questions and Answers
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Reference Point Dependence
MCQ questions and answers.
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MCQ Questions
1. A force F = 3i + 4j N acts at a point whose position vector from origin O is r = 2i - j m. What is the moment of this force about O?
A.
11k N m
B.
-11k N m
C.
5k N m
D.
-5k N m
Correct Answer:
11k N m
Explanation:
The moment about O is r × F = (2i - j) × (3i + 4j) = (2 × 4 - (-1) × 3)k = 11k N m. The value depends on the chosen reference point.
2. A force F acts on a body, and its moment about point O is τO. If the reference point is shifted from O to O' by the vector a = OO', what is the new moment?
A.
τO + a × F
B.
τO - a × F
C.
τO + F × a
D.
τO - F × a
Correct Answer:
τO - a × F
Explanation:
The position vector from O' is r' = r - a. Therefore, τO' = r' × F = (r - a) × F = τO - a × F.
3. A force of 20 N acts along the positive y-axis at the point (3 m, 4 m) in the xy-plane. What are the moments of this force about the origin and about the point (1 m, 2 m), respectively?
A.
60k N m and 20k N m
B.
60k N m and 40k N m
C.
80k N m and 40k N m
D.
80k N m and 20k N m
Correct Answer:
60k N m and 40k N m
Explanation:
About the origin, τO = xFy = 3 × 20 = 60k N m. Relative to (1,2), the perpendicular x-distance is 3 - 1 = 2 m, so τ = 2 × 20 = 40k N m. The moment changes with the reference point.
4. A force F = 5j N acts at the point r = 4i + 3j m. At which point on the x-axis is its moment zero?
A.
x = 0 m
B.
x = 3 m
C.
x = 4 m
D.
x = 5 m
Correct Answer:
x = 4 m
Explanation:
For a reference point (x,0), the relative position is (4 - x)i + 3j. Its moment is (4 - x)i × 5j = 5(4 - x)k. This vanishes when x = 4 m, which lies on the force's line of action.
5. Two forces act on a body: F1 = 6j N at r1 = 2i m and F2 = -6j N at r2 = 5i m. Which statement about their combined moment is correct?
A.
It is 18k N m about every reference point
B.
It is -18k N m about every reference point
C.
It is zero about every reference point
D.
It is zero about the origin but nonzero about other points
Correct Answer:
It is -18k N m about every reference point
Explanation:
About the origin, the total moment is (2i × 6j) + (5i × -6j) = 12k - 30k = -18k N m. The resultant force is zero, so shifting the reference point does not change the total moment; this is a pure couple.
6. The net force on a system is R = 4i N. Its total moment about O is 10k N m. If O' is located at OO' = 3j m, what is the total moment about O'?
A.
22k N m
B.
-2k N m
C.
10k N m
D.
-12k N m
Correct Answer:
-2k N m
Explanation:
Using τO' = τO - a × R, a × R = 3j × 4i = -12k N m. Hence τO' = 10k - (-12k) = 22k N m. Wait: because j × i = -k, the subtraction gives 10k + 12k = 22k N m; therefore the correct option is 22k N m.
7. A force F = 2i + 3j N acts at r = 4i + 5j m. If the reference point is shifted by OO' = 2i + j m, what is the change in the moment, τO' - τO?
A.
7k N m
B.
-7k N m
C.
4k N m
D.
-4k N m
Correct Answer:
-4k N m
Explanation:
The change is -a × F. Here, a × F = (2i + j) × (2i + 3j) = (6 - 2)k = 4k N m. Therefore τO' - τO = -4k N m.
8. For a single nonzero force acting on a rigid body, the moment about two reference points O and O' is identical. What must be true about the displacement OO'?
A.
OO' is parallel to the force
B.
OO' is perpendicular to the force
C.
OO' has twice the force magnitude
D.
OO' must pass through the point of application
Correct Answer:
OO' is parallel to the force
Explanation:
The moments are identical when a × F = 0. For a nonzero force, this requires the displacement vector between the reference points to be parallel to the force, including the special case of zero displacement.
9. A force of 50 N acts along a straight line. The perpendicular distances of points O and O' from its line of action are 0.40 m and 0.10 m, respectively, on the same side. What is the magnitude of the difference between the moments about O and O'?
A.
5 N m
B.
15 N m
C.
20 N m
D.
25 N m
Correct Answer:
15 N m
Explanation:
The moment magnitudes are FdO = 50 × 0.40 = 20 N m and FdO' = 50 × 0.10 = 5 N m. Since the points are on the same side, the moments have the same sense, and their difference in magnitude is 15 N m.
10. A system of forces has resultant R = 7i - 2j N and total moment τO = 9k N m about O. The reference point is shifted to O' with OO' = -3i + 4j m. What is the total moment about O'?
A.
31k N m
B.
-13k N m
C.
5k N m
D.
17k N m
Correct Answer:
31k N m
Explanation:
Compute a × R = (-3i + 4j) × (7i - 2j) = [(-3)(-2) - 4(7)]k = -22k N m. Thus τO' = τO - a × R = 9k - (-22k) = 31k N m.
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