physics : class11 Effect of Rod Orientation : Centre of Mass of a Uniform Rod : Motion of System of Particles and Rigid Body MCQ Questions and Answers
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Effect of Rod Orientation
MCQ questions and answers.
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MCQ Questions
1. A uniform rod of length 2 m is placed horizontally along the x-axis from x = 0 to x = 2 m. What is the x-coordinate of its centre of mass?
A.
0 m
B.
1 m
C.
2 m
D.
4 m
Correct Answer:
1 m
Explanation:
For a uniform rod, the centre of mass lies at its geometric midpoint. The midpoint of x = 0 m and x = 2 m is x = 1 m.
2. A uniform rod is placed vertically with its lower end at y = 0 m and upper end at y = 4 m. What is the y-coordinate of its centre of mass?
A.
0 m
B.
1 m
C.
2 m
D.
4 m
Correct Answer:
2 m
Explanation:
Changing the rod's orientation to vertical does not change the midpoint rule. The centre of mass is halfway between y = 0 m and y = 4 m, so y = 2 m.
3. A uniform rod has its endpoints at coordinates (1 m, 2 m) and (5 m, 2 m). Where is its centre of mass?
A.
(1 m, 2 m)
B.
(3 m, 2 m)
C.
(5 m, 2 m)
D.
(6 m, 4 m)
Correct Answer:
(3 m, 2 m)
Explanation:
The centre of mass of a uniform rod is at the midpoint of its endpoints. Averaging the coordinates gives ((1 + 5)/2, (2 + 2)/2) = (3 m, 2 m).
4. A uniform rod is rotated from a horizontal position to a vertical position about its centre. What happens to its centre of mass?
A.
It moves to one end of the rod
B.
It moves to the other end of the rod
C.
It remains at the centre of the rod
D.
It disappears during rotation
Correct Answer:
It remains at the centre of the rod
Explanation:
For a uniform rod, the centre of mass is always at its geometric centre, irrespective of whether the rod is horizontal, vertical, or inclined.
5. A uniform rod of length 6 m is inclined in any direction. How far is its centre of mass from either end?
A.
1 m
B.
2 m
C.
3 m
D.
6 m
Correct Answer:
3 m
Explanation:
The centre of mass of a uniform rod is its midpoint. Therefore, it is half the rod's length, or 6/2 = 3 m, from either end regardless of orientation.
6. A uniform rod lies along a straight line with endpoints at (0 m, 0 m) and (4 m, 3 m). What is the position of its centre of mass?
A.
(2 m, 1.5 m)
B.
(4 m, 3 m)
C.
(2 m, 3 m)
D.
(1 m, 2 m)
Correct Answer:
(2 m, 1.5 m)
Explanation:
The rod may be inclined, but its centre of mass is still the midpoint of its endpoints. Thus, the coordinates are ((0 + 4)/2, (0 + 3)/2) = (2 m, 1.5 m).
7. A uniform rod is placed at an angle of 30° to the horizontal. Where is its centre of mass located?
A.
At the lower end only
B.
At the upper end only
C.
At the midpoint of the rod
D.
Outside the rod
Correct Answer:
At the midpoint of the rod
Explanation:
The angle of inclination does not affect the location of the centre of mass along a uniform rod. It remains at the midpoint.
8. A uniform rod of length 10 m is vertical, with its lower end at y = 5 m. What is the y-coordinate of its centre of mass?
A.
5 m
B.
10 m
C.
15 m
D.
20 m
Correct Answer:
10 m
Explanation:
The upper end is at y = 15 m. The centre of mass is halfway between 5 m and 15 m, giving y = 10 m.
9. A uniform rod lies horizontally from x = -3 m to x = 1 m. What is the x-coordinate of its centre of mass?
A.
-3 m
B.
-2 m
C.
-1 m
D.
1 m
Correct Answer:
-1 m
Explanation:
The centre of mass is at the midpoint of the endpoints. Therefore, x = (-3 + 1)/2 = -1 m.
10. If a uniform rod is turned through any angle without changing its endpoints' midpoint, what happens to its centre of mass relative to the rod?
A.
It stays at one-quarter of the rod's length
B.
It stays at the midpoint of the rod
C.
It shifts toward the heavier end
D.
It shifts perpendicular to the rod
Correct Answer:
It stays at the midpoint of the rod
Explanation:
A uniform rod has equal mass distribution along its length. Therefore, its centre of mass remains at its midpoint for every orientation.
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