physics : class11 Centre of Mass at Midpoint : Centre of Mass of a Uniform Rod : Motion of System of Particles and Rigid Body MCQ Questions and Answers
Practice important
Centre of Mass at Midpoint
MCQ questions and answers.
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MCQ Questions
1. Where is the centre of mass of a uniform straight rod located?
A.
At one end of the rod
B.
At the midpoint of the rod
C.
At one-fourth of its length
D.
Outside the rod
Correct Answer:
At the midpoint of the rod
Explanation:
A uniform rod has its mass distributed equally on both sides, so its centre of mass lies at its geometric midpoint.
2. A uniform rod is 2 m long. How far is its centre of mass from either end?
A.
0.5 m
B.
1 m
C.
1.5 m
D.
2 m
Correct Answer:
1 m
Explanation:
The centre of mass of a uniform rod is at its midpoint. Half of 2 m is 1 m.
3. A uniform rod extends from x = 0 m to x = 6 m along the x-axis. What is the x-coordinate of its centre of mass?
A.
0 m
B.
2 m
C.
3 m
D.
6 m
Correct Answer:
3 m
Explanation:
The midpoint coordinate is the average of the endpoint coordinates: (0 + 6)/2 = 3 m.
4. A uniform rod has length L. Its centre of mass is located at a distance of:
A.
L from either end
B.
L/4 from either end
C.
L/2 from either end
D.
2L from either end
Correct Answer:
L/2 from either end
Explanation:
The midpoint divides the rod into two equal halves, so the centre of mass is L/2 from each end.
5. Why is the centre of mass of a uniform rod at its midpoint?
A.
The rod has equal mass distribution on both sides
B.
The rod has maximum mass at its centre
C.
The rod has no mass at its ends
D.
The rod is always moving
Correct Answer:
The rod has equal mass distribution on both sides
Explanation:
Uniform mass distribution gives equal amounts of mass at equal distances on opposite sides of the midpoint, placing the centre of mass there.
6. A uniform rod is 10 cm long. What is the position of its centre of mass measured from either end?
A.
2 cm
B.
5 cm
C.
8 cm
D.
10 cm
Correct Answer:
5 cm
Explanation:
The centre of mass lies at the midpoint, and half of 10 cm is 5 cm.
7. The endpoints of a uniform rod lie at x = 2 m and x = 8 m. Where is its centre of mass?
A.
x = 3 m
B.
x = 4 m
C.
x = 5 m
D.
x = 6 m
Correct Answer:
x = 5 m
Explanation:
The centre of mass is at the midpoint: (2 + 8)/2 = 5 m.
8. If a uniform rod is placed along the y-axis from y = -4 m to y = 4 m, what is the y-coordinate of its centre of mass?
A.
-4 m
B.
-2 m
C.
0 m
D.
4 m
Correct Answer:
0 m
Explanation:
The midpoint of -4 m and 4 m is 0 m, so the centre of mass is at the origin.
9. A uniform rod has its two ends at x = -3 m and x = 5 m. What is the x-coordinate of its centre of mass?
A.
-1 m
B.
0 m
C.
1 m
D.
2 m
Correct Answer:
1 m
Explanation:
The midpoint coordinate is (-3 + 5)/2 = 1 m, which is the centre of mass position.
10. If a uniform rod is divided into two equal parts at its centre, how are the masses of the two parts related?
A.
The first part has twice the mass of the second
B.
The second part has twice the mass of the first
C.
Both parts have equal mass
D.
One part has zero mass
Correct Answer:
Both parts have equal mass
Explanation:
For a uniform rod, equal lengths contain equal masses. Therefore, the midpoint divides the rod into two parts of equal mass.