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
Practice important
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 are the coordinates of its ends?
A.
(-L/2, 0) and (L/2, 0)
B.
(0, 0) and (L, 0)
C.
(-L, 0) and (L, 0)
D.
(L/2, 0) and (L, 0)
Correct Answer:
(-L/2, 0) and (L/2, 0)
Explanation:
Since the origin is at the centre of the rod, the rod extends equally on both sides. Each end is therefore at a distance L/2 from the origin.
2. The centre of mass of a uniform rod of length 2L is taken as the origin. What is the x-coordinate of its left end?
A.
0
B.
L
C.
-L
D.
-2L
Correct Answer:
-L
Explanation:
A rod of length 2L extends L on either side of its centre. Thus, with the centre at the origin, the left end has coordinate -L.
3. A uniform rod lies along the x-axis from x = -3 m to x = +3 m. Where is its centre of mass?
A.
At x = -3 m
B.
At x = 0 m
C.
At x = +3 m
D.
At x = +6 m
Correct Answer:
At x = 0 m
Explanation:
For a uniform rod, the centre of mass is at its geometrical centre. The interval from -3 m to +3 m has its centre at x = 0 m.
4. A uniform rod of length 10 cm has its centre at the origin. What is the coordinate of its right end?
A.
-10 cm
B.
-5 cm
C.
0 cm
D.
+5 cm
Correct Answer:
+5 cm
Explanation:
The rod extends half its length, 5 cm, on each side of the origin. Therefore, its right end is at x = +5 cm.
5. For a uniform rod placed symmetrically about the origin, the mass element at coordinate +x has a corresponding mass element at which coordinate?
A.
+2x
B.
0
C.
-x
D.
-2x
Correct Answer:
-x
Explanation:
Because the origin is at the centre of the uniform rod, equal mass elements occur at equal distances on opposite sides. Thus, the element at +x corresponds to one at -x.
6. A uniform rod extends from x = -L/2 to x = +L/2. What is the position of its centre of mass?
A.
x = -L/2
B.
x = 0
C.
x = L/2
D.
x = L
Correct Answer:
x = 0
Explanation:
The rod is symmetric about the origin, and for a uniform rod the centre of mass lies at its geometrical centre. Hence, x_CM = 0.
7. A uniform rod of length 4 m is centred at the origin. What is the distance of either end from the origin?
A.
1 m
B.
2 m
C.
4 m
D.
8 m
Correct Answer:
2 m
Explanation:
When the origin is at the rod centre, each end is located at half the rod length from the origin. Half of 4 m is 2 m.
8. If the ends of a uniform rod centred at the origin are at x = -a and x = +a, what is the length of the rod?
A.
a
B.
2a
C.
a/2
D.
4a
Correct Answer:
2a
Explanation:
The rod extends from -a to +a, so its length is the difference between the end coordinates: a - (-a) = 2a.
9. A uniform rod has its centre at the origin and its length is L. Which interval represents the coordinates of points on the rod along the x-axis?
A.
0 to L
B.
-L to 0
C.
-L/2 to +L/2
D.
-L to +L
Correct Answer:
-L/2 to +L/2
Explanation:
With the origin at the centre, the rod extends half its length in the positive direction and half in the negative direction. Therefore, its coordinates range from -L/2 to +L/2.
10. For a uniform rod centred at the origin, what is the average of the coordinates of its two ends?
A.
-L
B.
-L/2
C.
0
D.
L
Correct Answer:
0
Explanation:
The end coordinates are -L/2 and +L/2. Their average is [(-L/2) + (L/2)]/2 = 0, which is also the centre-of-mass coordinate.