physics : class11 Resultant Torque : Moment of a Force : Motion of System of Particles and Rigid Body MCQ Questions and Answers
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Resultant Torque
MCQ questions and answers.
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MCQ Questions
1. Three forces act in the xy-plane. A force F1 = (3i + 4j) N is applied at r1 = (2i - j) m, and a force F2 = (5i - 2j) N is applied at r2 = (-i + 2j) m. What is the resultant torque about the origin?
A.
+3 N·m in the +z direction
B.
-3 N·m in the +z direction
C.
+19 N·m in the +z direction
D.
-19 N·m in the +z direction
Correct Answer:
+3 N·m in the +z direction
Explanation:
For a planar force, τz = xFy − yFx. Thus τ1 = 2(4) − (−1)(3) = 11 N·m and τ2 = (−1)(−2) − 2(5) = −8 N·m. Therefore, the resultant torque is 11 − 8 = +3 N·m in the +z direction.
2. Four forces act at the points indicated by their position vectors from O: F1 = 4j N at r1 = 3i m, F2 = −5i N at r2 = 2j m, F3 = −2j N at r3 = −4i m, and F4 = 3i N at r4 = −j m. What is the resultant torque about O?
A.
−8 N·m in the z direction
B.
+8 N·m in the z direction
C.
+29 N·m in the z direction
D.
−29 N·m in the z direction
Correct Answer:
+8 N·m in the z direction
Explanation:
The individual torques are τ1 = 12k, τ2 = 10k, τ3 = 8k, and τ4 = 3k N·m. Hence the resultant torque is 12 + 10 + 8 + 3 = 33 N·m in the +z direction.
3. A force F = (6i + 8j) N is applied at the point r = (xi + 2j) m. If its torque about the origin is +20k N·m, what is the value of x?
A.
−2 m
B.
−1 m
C.
2 m
D.
4 m
Correct Answer:
2 m
Explanation:
Using τz = xFy − yFx, we get τz = 8x − 12. Equating this to 20 N·m gives 8x − 12 = 20, hence x = 4 m.
4. A system of forces has resultant force R = 5i N and resultant torque about O equal to 18k N·m. If the torque is required about a point O' whose position vector from O is a = 2j m, what is the resultant torque about O'?
A.
8k N·m
B.
18k N·m
C.
28k N·m
D.
−8k N·m
Correct Answer:
8k N·m
Explanation:
For a shifted origin, τO' = τO − a × R. Since a × R = 2j × 5i = −10k N·m, τO' = 18k − (−10k) = 28k N·m.
5. Two forces act on a body: F1 = (2i − 3j + k) N at r1 = (i + 2j) m and F2 = (−i + 4j + 2k) N at r2 = (2i − j + k) m. What is the resultant torque about the origin?
A.
−9i + 2j + 10k N·m
B.
9i − 2j − 10k N·m
C.
−9i − 2j + 10k N·m
D.
9i + 2j − 10k N·m
Correct Answer:
−9i + 2j + 10k N·m
Explanation:
Using the cross product, r1 × F1 = 2i − 5k N·m and r2 × F2 = −6i − 5j + 7k N·m. Hence the resultant torque is −4i − 5j + 2k N·m.
6. A force of magnitude 20 N acts at a point 0.40 m from O. The position vector makes 30° with the force. A second force produces a torque of 3 N·m in the opposite sense. What is the magnitude of the resultant torque about O?
A.
4 N·m
B.
7 N·m
C.
10 N·m
D.
13 N·m
Correct Answer:
7 N·m
Explanation:
The first torque is τ1 = rF sin 30° = 4 N·m. The torques oppose each other, so the resultant is |4 − 3| = 1 N·m.
7. A 10 N force acts at (3i + 4j) m and is directed along (4i − 3j). A second force acts at (−2i + j) m and is F2 = (6i + 8j) N. What is the resultant torque about the origin?
A.
−50 N·m
B.
−10 N·m
C.
+10 N·m
D.
+50 N·m
Correct Answer:
−50 N·m
Explanation:
The first force is F1 = 8i − 6j N, giving τ1 = 3(−6) − 4(8) = −50 N·m. The second gives τ2 = (−2)(8) − 1(6) = −22 N·m. Therefore, the resultant torque is −72 N·m.
8. A system consists of two equal and opposite parallel forces of 12 N whose lines of action are separated by 0.25 m, together with a 5 N·m torque acting in the same sense. What is the resultant torque?
A.
2 N·m
B.
3 N·m
C.
8 N·m
D.
17 N·m
Correct Answer:
8 N·m
Explanation:
The equal and opposite forces form a couple of torque Fd = 12 × 0.25 = 3 N·m. Since this couple and the applied torque act in the same sense, the resultant torque is 3 + 5 = 8 N·m.
9. For a system of coplanar forces, the resultant force is zero and the resultant torque about a point O is 14 N·m counterclockwise. What is the resultant torque about any other point in the plane?
A.
Zero
B.
14 N·m clockwise
C.
14 N·m counterclockwise
D.
It depends on the distance from O
Correct Answer:
14 N·m counterclockwise
Explanation:
When the resultant force is zero, shifting the origin does not change the resultant torque because τO' = τO − a × R and R = 0. Therefore, the torque remains 14 N·m counterclockwise about every point.
10. A force F = (4i + 3j) N acts at r = (2i − j) m, while another force of magnitude 10 N acts at r2 = (−i + 3j) m in a direction making 37° with the positive x-axis. Taking sin 37° = 3/5 and cos 37° = 4/5, what is the resultant torque about the origin?
A.
−21 N·m
B.
−9 N·m
C.
+9 N·m
D.
+21 N·m
Correct Answer:
−21 N·m
Explanation:
The first torque is 10 N·m. The second force has components 8i + 6j N and produces τ2 = −6 − 24 = −30 N·m. Thus, the resultant torque is −20 N·m.
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