1. A force has components F_x = 3 N and F_y = 4 N. Its position vector from the axis is r = 2 m along the x-axis. What is the torque about the origin?
A.
8 N m
B.
6 N m
C.
14 N m
D.
2 N m
Correct Answer:
8 N m
Explanation:
Using τ_z = xF_y - yF_x, with x = 2 m and y = 0, τ_z = 2 × 4 = 8 N m.
2. A force of components F_x = 5 N and F_y = 2 N acts at the point (3 m, 1 m). What is its torque about the origin?
A.
1 N m
B.
11 N m
C.
4 N m
D.
16 N m
Correct Answer:
1 N m
Explanation:
The torque is τ_z = xF_y - yF_x = (3 × 2) - (1 × 5) = 1 N m.
3. A force acts at the point (2 m, 4 m) with components F_x = 3 N and F_y = 1 N. What is the torque about the origin?
A.
10 N m
B.
-10 N m
C.
2 N m
D.
-2 N m
Correct Answer:
-10 N m
Explanation:
Using τ_z = xF_y - yF_x, τ_z = (2 × 1) - (4 × 3) = 2 - 12 = -10 N m.
4. A force with components F_x = 0 N and F_y = 6 N acts at a point 3 m from the origin along the x-axis. What is the magnitude of the torque?
A.
2 N m
B.
9 N m
C.
18 N m
D.
0 N m
Correct Answer:
18 N m
Explanation:
Since the point lies on the x-axis, τ_z = xF_y = 3 × 6 = 18 N m.
5. A force with components F_x = 4 N and F_y = 0 N acts at the point (0 m, 2 m). What is the torque about the origin?
A.
8 N m
B.
-8 N m
C.
2 N m
D.
0 N m
Correct Answer:
-8 N m
Explanation:
Using τ_z = xF_y - yF_x, τ_z = (0 × 0) - (2 × 4) = -8 N m.
6. A force acts at (2 m, 3 m) with components F_x = 1 N and F_y = 2 N. What is the torque about the origin?
A.
1 N m
B.
4 N m
C.
5 N m
D.
8 N m
Correct Answer:
1 N m
Explanation:
The torque is τ_z = xF_y - yF_x = (2 × 2) - (3 × 1) = 1 N m.
7. At the point (4 m, 2 m), a force has components F_x = 2 N and F_y = 3 N. What is the torque about the origin?
A.
4 N m
B.
8 N m
C.
10 N m
D.
16 N m
Correct Answer:
8 N m
Explanation:
Using τ_z = xF_y - yF_x, τ_z = (4 × 3) - (2 × 2) = 12 - 4 = 8 N m.
8. A force with F_x = 2 N and F_y = 5 N acts at a point on the y-axis 4 m from the origin. What is the torque about the origin?
A.
8 N m
B.
20 N m
C.
-8 N m
D.
12 N m
Correct Answer:
-8 N m
Explanation:
For a point on the y-axis, x = 0. Thus τ_z = 0 × 5 - 4 × 2 = -8 N m.
9. A force acts at the point (5 m, 0 m) with components F_x = 7 N and F_y = 2 N. What is the torque about the origin?
A.
10 N m
B.
14 N m
C.
35 N m
D.
7 N m
Correct Answer:
10 N m
Explanation:
Since y = 0, the torque is τ_z = xF_y = 5 × 2 = 10 N m. The x-component produces no torque here.
10. A force with components F_x = 6 N and F_y = 4 N acts at the point (1 m, 2 m). What is the torque about the origin?
A.
-8 N m
B.
8 N m
C.
14 N m
D.
-14 N m
Correct Answer:
-8 N m
Explanation:
Using τ_z = xF_y - yF_x, τ_z = (1 × 4) - (2 × 6) = 4 - 12 = -8 N m.
Short questions are currently unavailable for this page.