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
Practice important
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:
For a uniform rod, the mass is distributed equally along its length, so its centre of mass lies at the midpoint, a distance L/2 from either end.
2. A uniform rod has length 2 m. What is the distance of 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:
The centre of mass of a uniform rod is at its midpoint. Therefore, the distance is L/2 = 2/2 = 1 m.
3. A uniform rod of mass 5 kg and length 4 m is placed along a straight line. Its centre of mass is located at:
A.
1 m from either end
B.
2 m from either end
C.
4 m from either end
D.
5 m from either end
Correct Answer:
2 m from either end
Explanation:
The mass value does not change the centre-of-mass position for a uniform rod. The centre is at half its length, 4/2 = 2 m from either end.
4. A uniform rod of length 10 cm has its centre of mass at:
A.
2.5 cm from one end
B.
5 cm from one end
C.
10 cm from one end
D.
20 cm from one end
Correct Answer:
5 cm from one end
Explanation:
For a uniform rod, the centre of mass is at the midpoint. Half of 10 cm is 5 cm.
5. If the length of a uniform rod is doubled while its uniformity is unchanged, the centre of mass remains:
A.
At one end
B.
At one-fourth of the new length
C.
At the midpoint of the new length
D.
Outside the rod
Correct Answer:
At the midpoint of the new length
Explanation:
Changing the length does not alter the rule for a uniform rod. Its centre of mass is always located at half of its new length.
6. Two uniform rods have the same length but different masses. Their centres of mass are located:
A.
At different positions because their masses differ
B.
At the midpoint of each rod
C.
At the heavier end of each rod
D.
At the lighter end of each rod
Correct Answer:
At the midpoint of each rod
Explanation:
For a uniform rod, equal mass distribution along the length places the centre of mass at the midpoint, independent of the total mass.
7. A uniform rod of length 6 m is placed with one end at the origin along the positive x-axis. What is the x-coordinate of its centre of mass?
A.
1 m
B.
3 m
C.
6 m
D.
12 m
Correct Answer:
3 m
Explanation:
The rod extends from x = 0 to x = 6 m. Its centre of mass is at the midpoint, x = 6/2 = 3 m.
8. A uniform rod has mass 2 kg and length 8 m. If its mass is increased uniformly without changing its length, the centre of mass will be:
A.
At 2 m from an end
B.
At 4 m from an end
C.
At 8 m from an end
D.
At a position depending on the new mass
Correct Answer:
At 4 m from an end
Explanation:
Uniformly increasing the mass changes the total mass but not the symmetry of the distribution. The centre of mass remains at half the length, 8/2 = 4 m.
9. The centre of mass of a uniform rod of length L is located at a distance of:
A.
L from either end
B.
L/3 from either end
C.
L/2 from either end
D.
2L from either end
Correct Answer:
L/2 from either end
Explanation:
Since a uniform rod has identical mass distribution on both sides of its midpoint, its centre of mass is L/2 from either end.
10. A uniform rod of mass 10 kg and length 3 m is cut into two equal halves. The centre of mass of each half is located:
A.
At the end of each half
B.
At the midpoint of each half
C.
At the midpoint of the original rod for both halves
D.
Outside each half
Correct Answer:
At the midpoint of each half
Explanation:
Each half remains a uniform rod, so the centre of mass of each piece lies at its own midpoint, regardless of its mass.