physics : class11 Centre of Mass Formula : Centre of Mass of a Uniform Rod : Motion of System of Particles and Rigid Body MCQ Questions and Answers
Practice important
Centre of Mass Formula
MCQ questions and answers.
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MCQ Questions
1. What is the position of the centre of mass of a uniform rod of length L measured from either end?
A.
L/4
B.
L/2
C.
2L/3
D.
L
Correct Answer:
L/2
Explanation:
For a uniform rod, the centre of mass lies at its geometric centre. Therefore, its distance from either end is L/2.
2. A uniform rod extends from x = 0 to x = L along the x-axis. What is the x-coordinate of its centre of mass?
A.
0
B.
L/4
C.
L/2
D.
L
Correct Answer:
L/2
Explanation:
The centre of mass of a uniform rod is at its midpoint. The midpoint of x = 0 and x = L is x = L/2.
3. A uniform rod has length 2 m and lies along the x-axis from x = 1 m to x = 3 m. Its centre of mass is at:
A.
1 m
B.
1.5 m
C.
2 m
D.
3 m
Correct Answer:
2 m
Explanation:
For a uniform rod, the centre of mass is at the average of the coordinates of its ends: (1 + 3)/2 = 2 m.
4. The centre of mass of a uniform rod of mass M and length L is located at a distance of:
A.
M/2 from one end
B.
L/2 from one end
C.
ML from one end
D.
L/M from one end
Correct Answer:
L/2 from one end
Explanation:
The mass does not affect the position of the centre of mass of a uniform rod. It is located at the midpoint, a distance L/2 from either end.
5. A uniform rod extends from x = -L/2 to x = L/2. What is the coordinate of its centre of mass?
A.
-L/2
B.
-L/4
C.
0
D.
L/2
Correct Answer:
0
Explanation:
The centre of mass is at the midpoint of the rod. The midpoint of -L/2 and L/2 is 0.
6. A uniform rod of length 60 cm lies along a straight line. How far is its centre of mass from either end?
A.
15 cm
B.
20 cm
C.
30 cm
D.
60 cm
Correct Answer:
30 cm
Explanation:
The centre of mass of a uniform rod is at its midpoint, so its distance from either end is 60/2 = 30 cm.
7. If the ends of a uniform rod are at coordinates x1 and x2, the coordinate of its centre of mass is:
A.
x1 + x2
B.
x1x2
C.
(x1 + x2)/2
D.
(x2 - x1)/2
Correct Answer:
(x1 + x2)/2
Explanation:
For a uniform rod, the centre of mass is at the midpoint of its ends. The midpoint coordinate is (x1 + x2)/2.
8. A uniform rod is 4 m long and extends from x = 2 m to x = 6 m. What is the position of its centre of mass?
A.
2 m
B.
3 m
C.
4 m
D.
6 m
Correct Answer:
4 m
Explanation:
The centre of mass is at the midpoint of the rod: (2 + 6)/2 = 4 m.
9. For a uniform rod, the centre of mass is located at the point where:
A.
One-fourth of the length is measured from an end
B.
Half of the length is measured from either end
C.
The full length is measured from an end
D.
Two-thirds of the length is measured from an end
Correct Answer:
Half of the length is measured from either end
Explanation:
Uniform mass distribution makes the centre of mass coincide with the geometric midpoint, which is half the rod's length from either end.
10. A uniform rod extends from x = 5 m to x = 9 m. Using the centre of mass formula for a uniform rod, find its centre of mass coordinate.
A.
5 m
B.
6 m
C.
7 m
D.
9 m
Correct Answer:
7 m
Explanation:
The centre of mass coordinate is the midpoint of the two ends: (5 + 9)/2 = 7 m.