physics : class11 Rod Length and Mass : Centre of Mass of a Uniform Rod : Motion of System of Particles and Rigid Body MCQ Questions and Answers
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Rod Length and Mass
MCQ questions and answers.
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MCQ Questions
1. Where is the centre of mass of a uniform rod of length L 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 along its length, so its centre of mass lies at its geometrical midpoint, a distance L/2 from either end.
2. A uniform rod has a length of 2 m. How far is its centre of mass from either end?
A.
0.5 m
B.
1 m
C.
2 m
D.
4 m
Correct Answer:
1 m
Explanation:
For a uniform rod, the centre of mass is at half its length. Thus, distance = 2/2 = 1 m.
3. A uniform rod is 80 cm long. Its centre of mass is located how far from one end?
A.
20 cm
B.
40 cm
C.
60 cm
D.
80 cm
Correct Answer:
40 cm
Explanation:
The centre of mass of a uniform rod is at its midpoint, so its distance from either end is 80/2 = 40 cm.
4. If the length of a uniform rod is doubled while its uniform mass distribution is maintained, the distance of its centre of mass from either end becomes:
A.
Half as large
B.
Unchanged
C.
Twice as large
D.
Four times as large
Correct Answer:
Twice as large
Explanation:
The centre of mass is located at half the rod's length. Doubling the length doubles the distance from either end to the centre of mass.
5. A uniform rod of mass 6 kg and length 3 m has its centre of mass at:
A.
0.5 m from either end
B.
1 m from either end
C.
1.5 m from either end
D.
3 m from either end
Correct Answer:
1.5 m from either end
Explanation:
For a uniform rod, the centre of mass depends on its length and is at L/2 = 3/2 = 1.5 m from either end.
6. For a uniform rod, changing its total mass while keeping its length unchanged will cause the centre of mass to:
A.
Move to the left end
B.
Move to the right end
C.
Remain at the midpoint
D.
Move outside the rod
Correct Answer:
Remain at the midpoint
Explanation:
Changing the total mass uniformly changes the amount of mass but not its symmetric distribution, so the centre of mass remains at the midpoint.
7. A uniform rod has length 1.2 m. Measured from one end, the position of its centre of mass is:
A.
0.2 m
B.
0.4 m
C.
0.6 m
D.
1.2 m
Correct Answer:
0.6 m
Explanation:
The centre of mass of a uniform rod is at half its length. Therefore, its position is 1.2/2 = 0.6 m from either end.
8. Two uniform rods have the same length but different masses. Their centres of mass are located:
A.
At different points because their masses differ
B.
At the midpoint of each rod
C.
At the heavier rod's end
D.
Outside both rods
Correct Answer:
At the midpoint of each rod
Explanation:
For each uniform rod, equal distribution along its length places the centre of mass at the midpoint, regardless of its total mass.
9. A uniform rod of length 50 cm has its centre of mass at a distance of how many centimetres from its left end?
A.
10 cm
B.
20 cm
C.
25 cm
D.
50 cm
Correct Answer:
25 cm
Explanation:
The centre of mass is at the midpoint of the rod, so its distance from the left end is 50/2 = 25 cm.
10. A uniform rod has its centre of mass 3 m from either end. What is the length of the rod?
A.
1.5 m
B.
3 m
C.
6 m
D.
9 m
Correct Answer:
6 m
Explanation:
The centre of mass is at half the rod's length. If the distance from an end is 3 m, then the total length is 2 × 3 = 6 m.