1. A uniform rod lies along the y-axis from y = 0 to y = L. What is the y-coordinate of its centre of mass?
A.
0
B.
L/4
C.
L/2
D.
L
Correct Answer:
L/2
Explanation:
For a uniform rod, the centre of mass lies at its geometric midpoint. The midpoint of y = 0 and y = L is y = L/2.
2. A uniform rod extends along the y-axis from y = 2 m to y = 8 m. Where is its centre of mass?
A.
y = 2 m
B.
y = 4 m
C.
y = 5 m
D.
y = 8 m
Correct Answer:
y = 5 m
Explanation:
The centre of mass of a uniform rod is at the average of the coordinates of its ends: (2 + 8)/2 = 5 m.
3. A uniform rod of length 4 m is placed along the y-axis with its lower end at y = -2 m. What is the y-coordinate of its centre of mass?
A.
-4 m
B.
-2 m
C.
0 m
D.
2 m
Correct Answer:
0 m
Explanation:
The upper end is at y = -2 + 4 = 2 m. The centre of mass is at the midpoint, (−2 + 2)/2 = 0 m.
4. A uniform rod lies along the y-axis from y = -L to y = L. What is the position of its centre of mass?
A.
At y = -L
B.
At y = -L/2
C.
At y = 0
D.
At y = L
Correct Answer:
At y = 0
Explanation:
The rod is symmetric about the origin, so its geometric midpoint and centre of mass are at y = 0.
5. A uniform rod along the y-axis has ends at y = 3 m and y = 11 m. What is the distance of its centre of mass from the origin?
A.
3 m
B.
4 m
C.
7 m
D.
11 m
Correct Answer:
7 m
Explanation:
The centre of mass is at the midpoint: y = (3 + 11)/2 = 7 m. Its distance from the origin is therefore 7 m.
6. For a uniform rod placed along the y-axis, the x-coordinate of its centre of mass is:
A.
Equal to its length
B.
Half its length
C.
Zero if the rod lies on the y-axis
D.
Always equal to 1 m
Correct Answer:
Zero if the rod lies on the y-axis
Explanation:
Every point of a rod lying along the y-axis has x-coordinate zero. Hence, the centre of mass also has x-coordinate zero.
7. A uniform rod of length 10 cm lies along the positive y-axis with one end at the origin. What is the position of its centre of mass?
A.
At y = 2.5 cm
B.
At y = 5 cm
C.
At y = 10 cm
D.
At y = 20 cm
Correct Answer:
At y = 5 cm
Explanation:
The rod extends from y = 0 to y = 10 cm. Its centre of mass is at the midpoint, y = 10/2 = 5 cm.
8. A uniform rod along the y-axis has its ends at y = -6 m and y = -2 m. What is the y-coordinate of its centre of mass?
A.
-8 m
B.
-6 m
C.
-4 m
D.
-2 m
Correct Answer:
-4 m
Explanation:
The centre of mass is at the midpoint of the two ends: y = (−6 − 2)/2 = −4 m.
9. If a uniform rod along the y-axis has its centre of mass at y = 4 m and one end at y = 1 m, where is the other end?
A.
y = 2 m
B.
y = 5 m
C.
y = 7 m
D.
y = 8 m
Correct Answer:
y = 7 m
Explanation:
For a uniform rod, the centre of mass is the midpoint. Thus, 4 = (1 + y)/2, giving y = 7 m.
10. A uniform rod lies along the y-axis from y = 5 m to y = 9 m. What is the distance of its centre of mass from the lower end?
A.
1 m
B.
2 m
C.
4 m
D.
7 m
Correct Answer:
2 m
Explanation:
The centre of mass of a uniform rod is at its midpoint, so it is half the rod's length from either end. Half of 4 m is 2 m.
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