physics : class11 Rod Along the Y-Axis : Centre of Mass of a Uniform Rod : Motion of System of Particles and Rigid Body MCQ Questions and Answers
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Rod Along the Y-Axis
MCQ questions and answers.
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MCQ Questions
1. A uniform rod of length L lies along the y-axis with its ends at y = 0 and y = L. What is the y-coordinate of its centre of mass?
A.
0
B.
L/4
C.
L/2
D.
L
Correct Answer:
L/2
Explanation:
For a uniform rod, the centre of mass lies at its geometrical midpoint. The midpoint of y = 0 and y = L is y = L/2.
2. A uniform rod lies along the y-axis from y = -L/2 to y = L/2. Where is its centre of mass located?
A.
At y = -L/2
B.
At y = 0
C.
At y = L/4
D.
At y = L/2
Correct Answer:
At y = 0
Explanation:
The centre of mass of a uniform rod is at its midpoint. The midpoint of -L/2 and L/2 is y = 0.
3. A uniform rod of length 4 m is placed along the y-axis with one end at the origin and the other at y = 4 m. What is the position of its centre of mass?
A.
At y = 1 m
B.
At y = 2 m
C.
At y = 3 m
D.
At y = 4 m
Correct Answer:
At y = 2 m
Explanation:
The centre of mass of a uniform rod is halfway between its ends. Thus, y = (0 + 4)/2 = 2 m.
4. A uniform rod along the y-axis has its lower end at y = 2 m and upper end at y = 8 m. What is the y-coordinate of its centre of mass?
A.
2 m
B.
3 m
C.
5 m
D.
8 m
Correct Answer:
5 m
Explanation:
For a uniform rod, the centre of mass is at the average of the endpoint coordinates: y = (2 + 8)/2 = 5 m.
5. For a uniform rod placed along the y-axis, the x-coordinate of its centre of mass is what if the rod lies exactly on the y-axis?
A.
-L/2
B.
0
C.
L/2
D.
L
Correct Answer:
0
Explanation:
Every point of the rod has x-coordinate zero because it lies on the y-axis. Therefore, the centre of mass also has x-coordinate zero.
6. A uniform rod extends along the y-axis from y = 3 m to y = 7 m. What is the y-coordinate of its centre of mass?
A.
3 m
B.
4 m
C.
5 m
D.
7 m
Correct Answer:
5 m
Explanation:
The centre of mass is at the midpoint of the rod, so y = (3 + 7)/2 = 5 m.
7. A uniform rod of length L lies along the y-axis with its centre at the origin. What are the coordinates of its centre of mass?
A.
(L/2, 0)
B.
(0, L/2)
C.
(0, 0)
D.
(L, 0)
Correct Answer:
(0, 0)
Explanation:
Since the rod is uniform, its centre of mass is at its geometric centre. The geometric centre is given as the origin.
8. A uniform rod lies along the y-axis between y = -2 m and y = 6 m. What is the y-coordinate of its centre of mass?
A.
-2 m
B.
0 m
C.
2 m
D.
6 m
Correct Answer:
2 m
Explanation:
The midpoint of the endpoints is y = (-2 + 6)/2 = 2 m, which is the centre-of-mass coordinate.
9. A uniform rod of length 10 cm lies along the positive y-axis with one end at the origin. How far is its centre of mass from the origin?
A.
2.5 cm
B.
5 cm
C.
7.5 cm
D.
10 cm
Correct Answer:
5 cm
Explanation:
The centre of mass of a uniform rod is at its midpoint. Therefore, its distance from the origin is 10/2 = 5 cm.
10. A uniform rod along the y-axis has endpoints at (0, 1 m) and (0, 9 m). What are the coordinates of its centre of mass?
A.
(0, 1 m)
B.
(0, 4 m)
C.
(0, 5 m)
D.
(0, 9 m)
Correct Answer:
(0, 5 m)
Explanation:
The centre of mass is at the midpoint of the endpoints. Its coordinates are x = 0 and y = (1 + 9)/2 = 5 m.