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. The centre of mass of a uniform rod of length L placed along the x-axis from x = 0 to x = L is located at
A.
x = 0
B.
x = L/4
C.
x = L/2
D.
x = L
Correct Answer:
x = L/2
Explanation:
For a uniform rod, the centre of mass lies at its geometrical midpoint. The midpoint of the positions 0 and L is x = (0 + L)/2 = L/2.
2. A uniform rod extends from x = 2 m to x = 10 m. What is the x-coordinate of its centre of mass?
A.
4 m
B.
6 m
C.
8 m
D.
12 m
Correct Answer:
6 m
Explanation:
The centre of mass of a uniform rod is at the average of the coordinates of its ends: x_cm = (2 + 10)/2 = 6 m.
3. A uniform rod has its ends at x = -4 m and x = 6 m. Its centre of mass is at
A.
-5 m
B.
-1 m
C.
1 m
D.
2 m
Correct Answer:
1 m
Explanation:
Using the centre of mass formula for a uniform rod, x_cm = (x_1 + x_2)/2 = (-4 + 6)/2 = 1 m.
4. If a uniform rod of length 2 m is placed along the y-axis from y = 3 m to y = 5 m, its centre of mass is at
A.
y = 3 m
B.
y = 4 m
C.
y = 5 m
D.
y = 8 m
Correct Answer:
y = 4 m
Explanation:
For a uniform rod, the centre of mass is at the midpoint of its ends. Thus, y_cm = (3 + 5)/2 = 4 m.
5. The centre of mass of a uniform rod of length L is located from either end at a distance of
A.
L
B.
L/2
C.
L/3
D.
2L
Correct Answer:
L/2
Explanation:
Because the rod is uniform, its centre of mass lies at its midpoint. The distance from either end to the midpoint is L/2.
6. A uniform rod extends from x = -3 m to x = 3 m. What is the position of its centre of mass?
A.
x = -3 m
B.
x = -1.5 m
C.
x = 0 m
D.
x = 3 m
Correct Answer:
x = 0 m
Explanation:
The centre of mass is the average of the end coordinates: x_cm = (-3 + 3)/2 = 0 m.
7. A uniform rod has length 8 m and its left end is at x = 5 m. The x-coordinate of its centre of mass is
A.
5 m
B.
8 m
C.
9 m
D.
13 m
Correct Answer:
9 m
Explanation:
The right end is at x = 5 + 8 = 13 m. Therefore, x_cm = (5 + 13)/2 = 9 m.
8. For a uniform rod whose ends have position vectors r1 and r2, the position vector of its centre of mass is
A.
r1 + r2
B.
r1 - r2
C.
(r1 + r2)/2
D.
2(r1 + r2)
Correct Answer:
(r1 + r2)/2
Explanation:
For a uniform rod, equal mass is distributed symmetrically between its ends. Hence, its centre of mass position vector is the average of the end position vectors.
9. A uniform rod is 10 m long and extends from x = 4 m to x = 14 m. Its centre of mass is located at
A.
x = 5 m
B.
x = 9 m
C.
x = 10 m
D.
x = 14 m
Correct Answer:
x = 9 m
Explanation:
The centre of mass is at the midpoint of the rod: x_cm = (4 + 14)/2 = 9 m.
10. A uniform rod extends from x = -2 m to x = 8 m. What is the distance of its centre of mass from the origin?
A.
2 m
B.
3 m
C.
5 m
D.
8 m
Correct Answer:
3 m
Explanation:
The centre of mass coordinate is x_cm = (-2 + 8)/2 = 3 m. Therefore, its distance from the origin is 3 m.