physics : class11 Origin at Rod Centre : Centre of Mass of a Uniform Rod : Motion of System of Particles and Rigid Body MCQ Questions and Answers
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Origin at Rod Centre
MCQ questions and answers.
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MCQ Questions
1. A uniform rod of length L is placed along the x-axis with its centre at the origin. What is the x-coordinate of its centre of mass?
A.
0
B.
L/2
C.
-L/2
D.
L
Correct Answer:
0
Explanation:
For a uniform rod, the centre of mass lies at its geometrical centre. Since the rod's centre is at the origin, its x-coordinate is 0.
2. A uniform rod of length 2 m has its centre at the origin and lies along the x-axis. What are the coordinates of its ends?
A.
(1 m, 0) and (-1 m, 0)
B.
(2 m, 0) and (-2 m, 0)
C.
(0, 1 m) and (0, -1 m)
D.
(0.5 m, 0) and (-0.5 m, 0)
Correct Answer:
(1 m, 0) and (-1 m, 0)
Explanation:
The rod extends equally on both sides of the origin. Half its length is 1 m, so its ends are at x = +1 m and x = -1 m.
3. A uniform rod extends from x = -3 m to x = +3 m along the x-axis. Where is its centre of mass?
A.
At x = -3 m
B.
At x = 0
C.
At x = +3 m
D.
At x = +6 m
Correct Answer:
At x = 0
Explanation:
The rod is uniform and extends symmetrically from -3 m to +3 m. Its centre of mass is at the midpoint, x = 0.
4. A uniform rod is centred at the origin and lies along the y-axis. What is the y-coordinate of its centre of mass?
A.
Equal to the rod's length
B.
Half the rod's length
C.
0
D.
Negative of the rod's length
Correct Answer:
0
Explanation:
Because the rod is uniform and extends equally above and below the origin, its centre of mass is at y = 0.
5. A uniform rod of length L is placed along the x-axis from x = -L/2 to x = +L/2. What is the position of its centre of mass?
A.
x = -L/2
B.
x = L/4
C.
x = 0
D.
x = L/2
Correct Answer:
x = 0
Explanation:
The limits -L/2 and +L/2 are symmetric about the origin. Therefore, the centre of mass of the uniform rod is at x = 0.
6. For a uniform rod centred at the origin, what can be said about the mass distribution on its two sides?
A.
The entire mass is on the positive side
B.
The mass is equally distributed on both sides
C.
The entire mass is on the negative side
D.
The mass is concentrated only at the origin
Correct Answer:
The mass is equally distributed on both sides
Explanation:
A uniform rod centred at the origin has equal lengths and equal masses on its positive and negative sides, making its centre of mass the origin.
7. A uniform rod extends from x = -2 m to x = +2 m. What is the distance of its centre of mass from the origin?
A.
0 m
B.
1 m
C.
2 m
D.
4 m
Correct Answer:
0 m
Explanation:
The centre of mass is exactly at the origin because the rod is uniform and symmetric about the origin. Hence, its distance from the origin is 0 m.
8. A uniform rod of length 10 cm is centred at the origin along the x-axis. What is the x-coordinate of its left end?
A.
10 cm
B.
5 cm
C.
-5 cm
D.
-10 cm
Correct Answer:
-5 cm
Explanation:
The rod extends 5 cm on either side of its centre. Therefore, its left end is at x = -5 cm.
9. A uniform rod has its centre at the origin and its ends at x = -L/2 and x = +L/2. What is the average position of its ends along the x-axis?
A.
-L
B.
-L/2
C.
0
D.
L/2
Correct Answer:
0
Explanation:
The average of the end positions is [(-L/2) + (L/2)]/2 = 0. This is also the position of the centre of mass for a uniform rod.
10. If the origin is chosen at the centre of a uniform rod lying along the x-axis, what is the symmetry property of the rod's coordinates?
A.
Every positive coordinate has an equal negative coordinate
B.
All coordinates are positive
C.
All coordinates are negative
D.
Every coordinate is equal to the rod's length
Correct Answer:
Every positive coordinate has an equal negative coordinate
Explanation:
With the origin at the rod's centre, the rod extends equally in the positive and negative x-directions. Thus, each positive coordinate has a corresponding negative coordinate of equal magnitude.