1. A uniform rod has a length of 2 m. What is the distance of its centre of mass from either end?
A.
0.5 m
B.
1 m
C.
1.5 m
D.
2 m
Correct Answer:
1 m
Explanation:
For a uniform rod, the centre of mass lies at its midpoint. Therefore, its distance from either end is L/2 = 2/2 = 1 m.
2. The centre of mass of a uniform rod of length L is located at a distance of:
A.
L from one end
B.
L/3 from one end
C.
L/2 from one end
D.
2L from one end
Correct Answer:
L/2 from one end
Explanation:
A uniform rod has its mass distributed symmetrically, so its centre of mass is at the midpoint, which is L/2 from either end.
3. A uniform rod is 80 cm long. How far is its centre of mass from either end?
A.
20 cm
B.
30 cm
C.
40 cm
D.
80 cm
Correct Answer:
40 cm
Explanation:
The centre of mass of a uniform rod is at its midpoint. Hence, the distance from either end is 80/2 = 40 cm.
4. A uniform rod has its centre of mass 3 m from one 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 length of a uniform rod. Thus, L/2 = 3 m, giving L = 6 m.
5. For a uniform rod of length 1.2 m, the distance of the centre of mass from the left end is:
A.
0.3 m
B.
0.6 m
C.
0.9 m
D.
1.2 m
Correct Answer:
0.6 m
Explanation:
Since the rod is uniform, its centre of mass lies at the midpoint. The distance is 1.2/2 = 0.6 m from the left end.
6. If the centre of mass of a uniform rod is 25 cm from its right end, what is the length of the rod?
A.
12.5 cm
B.
25 cm
C.
50 cm
D.
75 cm
Correct Answer:
50 cm
Explanation:
For a uniform rod, the centre of mass is halfway between the ends. Therefore, L/2 = 25 cm, so L = 50 cm.
7. A uniform rod of length 10 m extends from x = 0 m to x = 10 m. What is the distance of its centre of mass from the end at x = 0 m?
A.
0 m
B.
2.5 m
C.
5 m
D.
10 m
Correct Answer:
5 m
Explanation:
The centre of mass of a uniform rod is at its midpoint. The midpoint of the rod is 10/2 = 5 m from the end at x = 0 m.
8. A uniform rod is 36 cm long. The centre of mass is located how far from its left end?
A.
9 cm
B.
12 cm
C.
18 cm
D.
24 cm
Correct Answer:
18 cm
Explanation:
The centre of mass lies at the midpoint of a uniform rod. Therefore, its distance from the left end is 36/2 = 18 cm.
9. Which statement correctly describes the position of the centre of mass of a uniform rod?
A.
It is at one end of the rod
B.
It is one-fourth of the length from one end
C.
It is at the midpoint of the rod
D.
It is outside the rod
Correct Answer:
It is at the midpoint of the rod
Explanation:
Because the mass of a uniform rod is distributed evenly, the centre of mass is located at its midpoint, at equal distance from both ends.
10. The distance of the centre of mass from either end of a uniform rod is 7.5 cm. What is the rod's length?
A.
7.5 cm
B.
10 cm
C.
15 cm
D.
30 cm
Correct Answer:
15 cm
Explanation:
The distance from either end to the centre of mass is half the rod's length. Thus, L = 2 × 7.5 cm = 15 cm.
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