physics : class11 Effect of Translation : 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 Translation
MCQ questions and answers.
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MCQ Questions
1. A uniform rod has its centre of mass at x = 2 m. If the entire rod is translated 5 m to the right without changing its orientation, what is the new position of its centre of mass?
A.
2 m
B.
3 m
C.
5 m
D.
7 m
Correct Answer:
7 m
Explanation:
During translation, every point of the rod, including its centre of mass, moves through the same displacement. Therefore, the new position is 2 m + 5 m = 7 m.
2. A uniform rod of length 4 m has its centre of mass at its midpoint. If the rod is translated 3 m to the left, how far does its centre of mass move?
A.
1 m to the left
B.
3 m to the left
C.
4 m to the left
D.
7 m to the left
Correct Answer:
3 m to the left
Explanation:
In a pure translation, the centre of mass undergoes the same displacement as the entire rod. Hence, it moves 3 m to the left.
3. A uniform rod lies along the x-axis with its centre of mass at x = 0.5 m. The rod is translated by 2 m in the positive x-direction. What is the new x-coordinate of its centre of mass?
A.
0.25 m
B.
0.5 m
C.
2.0 m
D.
2.5 m
Correct Answer:
2.5 m
Explanation:
Translation shifts the centre of mass by the same amount as the rod. Thus, the new coordinate is 0.5 m + 2 m = 2.5 m.
4. When a uniform rod is translated without rotation, what happens to the position of its centre of mass relative to the rod?
A.
It remains at the midpoint of the rod
B.
It moves to one end of the rod
C.
It moves outside the rod
D.
It shifts toward the heavier end
Correct Answer:
It remains at the midpoint of the rod
Explanation:
A uniform rod has its centre of mass at its midpoint. Translation changes the rod's overall position but does not change the centre of mass relative to the rod.
5. A uniform rod is translated 6 m upward without changing its orientation. If its centre of mass was at height 1 m, what is its new height?
A.
1 m
B.
5 m
C.
6 m
D.
7 m
Correct Answer:
7 m
Explanation:
The centre of mass moves upward by the same 6 m translation as the rod. Its new height is 1 m + 6 m = 7 m.
6. A uniform rod is translated horizontally while maintaining its orientation. Which quantity remains unchanged?
A.
The position of the rod in space
B.
The position of its centre of mass in space
C.
The distance of the centre of mass from either end
D.
The coordinates of every point in space
Correct Answer:
The distance of the centre of mass from either end
Explanation:
Translation moves all points by the same amount, so the centre of mass remains at the midpoint. Therefore, its distances from both ends remain unchanged.
7. A uniform rod has its centre of mass at x = 4 m. If the rod is translated 2 m in the negative x-direction, what is the new position of its centre of mass?
A.
2 m
B.
4 m
C.
6 m
D.
-2 m
Correct Answer:
2 m
Explanation:
The centre of mass undergoes the same displacement as the rod. Therefore, its new position is 4 m - 2 m = 2 m.
8. A uniform rod is translated with constant velocity without rotating. How does its centre of mass move?
A.
It remains at rest
B.
It moves with the same constant velocity
C.
It moves with increasing velocity
D.
It moves in a circular path
Correct Answer:
It moves with the same constant velocity
Explanation:
In translation, every point of the rod has the same velocity. Therefore, the centre of mass also moves with that same constant velocity.
9. A uniform rod is shifted 4 m to the right without rotation. What is the displacement of its centre of mass?
A.
Zero
B.
2 m to the right
C.
4 m to the right
D.
8 m to the right
Correct Answer:
4 m to the right
Explanation:
The centre of mass experiences the same displacement as the rod during translation. Hence, its displacement is 4 m to the right.
10. A uniform rod of length 10 m is translated without rotation. Initially, its centre of mass is 5 m from either end. After translation, what is its distance from either end?
A.
0 m
B.
2.5 m
C.
5 m
D.
10 m
Correct Answer:
5 m
Explanation:
Translation changes the location of the rod but not the relative positions of its points. The centre of mass of a uniform rod remains at its midpoint, 5 m from either end.
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