This set of Strength of Materials Assessment Questions and Answers on “Center of Gravity of Section”.
1. The center of gravity of the rod shown in figure will be _____________
a) 5cm
b) 10cm
c) 15cm
d) 20cm
Answer: b
Clarification: The center of gravity of a rod will be on its center. Here it will be at 10cm.
2. The center of gravity of a circle of radius 10 cm will be _____________
a) At its center of the diameter
b) At the center of the radius
c) Anywhere on the circumference
d) Anywhere in its area
Answer: a
Clarification: The whole weight of a circle can be assumed to act through its center. So the center of gravity of a circle is at its center. Whatever may be the radius of the circle the center of gravity will be on its center.
3. A rectangle has dimension of 10cm x 20cm. where will be its center of gravity?
a) (10,10)
b) (20,5)
c) (10,5)
d) (5,10)
Answer: c
Clarification: The centre of gravity of this rectangular area will be half of 10cm from x-axis and half of 20cm from y-axis. therefore the center of gravity will be at (10,5).
4. Where will be the centre of gravity of the T section shown in the figure?
a) 8
b) 8.5
c) 10.5
d) 11.5
Answer: d
Clarification: The center of gravity is given by, y = (a1y1 + a2y2) / (a1 + a2) = (100×17.5 + 150×7.5) / (100+150) = 11.5cm.
5. Where will be the center of gravity of the L-section shown in figure?
a) (4.33, 2.33)
b) (4, 6)
c) (2.33, 4.33)
d) (1, 5)
Answer: c
Clarification: The center of gravity is given by, y = (a1y1 + a2y2) / (a1 + a2) = (20×7 + 16×1) / (20+16) = 4.33cm.
This will on for the y-axis.
For the x-axis, The center of gravity is given by, x = (a1x1 + a2x2) / (a1 + a2) = (20×1 + 16×4) / (20+16) = 2.33cm.
So the center of gravity will be at (2.33, 4.33).
6. Where will be the center of gravity of the figure shown?
a) (3.45,4.52)
b) (3.59,4.52)
c) (3.66,5.17)
d) (4.01,5.15)
Answer: b
Clarification: Area of triangle = 20, area of rectangle = 50
The center of gravity is given by, y = (a1y1 + a2y2) / (a1 + a2) = (20×10/3 + 50×5) / (20+50) = 4.52cm.
This will on for the y-axis.
For the x-axis, The center of gravity is given by, x = (a1x1 + a2x2) / (a1 + a2) = (20×6.33 + 50×2.5) / (20+50) = 3.59cm.
So the center of gravity will be at (2.33, 4.33).
7. Where will be the center of gravity of the shown figure?
a) (4.66,6.332)
b) (4.34,3.24)
c) (4.25,6.45)
d) (4.87,6.41)
Answer: a
Clarification: Area of triangle = 25, area of rectangle = 100
The center of gravity is given by, y = (a1y1 + a2y2) / (a1 + a2) = (25×10/3 + 100×5) / (25+100) = 4.66cm.
This will on for the y-axis.
For the x-axis, The center of gravity is given by, x = (a1x1 + a2x2) / (a1 + a2) = (25×11.66 + 100×5) / (25+100) = 6.332cm.
So the center of gravity will be at (2.33, 4.33).
8. Where will be the center of gravity of an I section will be if the dimension of web is 2x20cm and that of flange is 2x15cm If the y-axis will pass through the center of the section?
a) 8.5cm
b) 9.5cm
c) 10.5cm
d) 11.5cm
Answer: b
Clarification: The center of gravity is given by, y = (a1y1 + a2y2 + a3y3) / (a1 + a2 + a3) = (40×18 + 30×9.5 +40×1 / (40 +30+40) = 9.5cm.
9. Where will be the center of gravity of an T section will be if the dimension of web is 2x20cm and that of flange is 2x15cm If the y-axis will pass through the center of the section?
a) 10.5cm
b) 11.45cm
c) 12.35cm
d) 12.85cm
Answer: b
Clarification: The center of gravity is given by, y = (a1y1 + a2y2) / (a1 + a2) = (40×16 + 30×7.5)/ (30+40) = 12.35cm.
10. Where will be the center of gravity of the following section?
a) 7.33cm
b) 8.33cm
c) 9.33cm
d) 10.33
Answer: b
Clarification: Area of triangle = 50, area of rectangle = 50
The center of gravity is given by, y = (a1y1 + a2y2) / (a1 + a2) = (50×11.66 + 50×5)/(50+50) = 8.33cm.
11. Where will be the centre of gravity of the following L-section?
a) (18.31,30.81)
b) (19.45, 29.87)
c) (20,30)
d) (19.62,29.62)
Answer: a
Clarification: The center of gravity is given by, y = (a1y1 + a2y2) / (a1 + a2) = (600×50 + 414×3) / (600+414) = 18.31cm.
This will on for the y-axis.
For the x-axis, The center of gravity is given by, x = (a1x1 + a2x2) / (a1 + a2) = (600×3 + 414×40.5) / (600+414) = 30.81cm.
So the center of gravity will be at (2.33, 4.33).
12. Where will be the center of gravity of an I section will be if the dimension of upper web is 2x8cm, lower web is 2×16 and that of flange is 2x12cm If the y-axis will pass through the center of the section?
a) 7.611cm
b) 7.44cm
c) 6.53cm
d) 6.44cm
Answer: d
Clarification: Area of upper web a1 = 16cm, area of flange a2 = 24, area of lower web a3 = 32.
The center of gravity is given by, y = (a1y1 + a2y2 + a3y3) / (a1 + a2 + a3) = (16×15 + 24×8 +32×1 / (16 +24+32)) = 6.44cm.
Strength of Materials Assessment Questions,