This set of Strength of Materials Assessment Questions and Answers focuses 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

View Answer

Explanation: 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

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Explanation: 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)

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Explanation: 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

View Answer

Explanation: The center of gravity is given by, y = (a

_{1}y

_{1}+ a

_{2}y

_{2}) / (a

_{1}+ a

_{2}) = (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)

View Answer

Explanation: The center of gravity is given by, y = (a

_{1}y

_{1}+ a

_{2}y

_{2}) / (a

_{1}+ a

_{2}) = (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 = (a

_{1}x

_{1}+ a

_{2}x

_{2}) / (a

_{1}+ a

_{2}) = (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)

View Answer

Explanation: Area of triangle = 20, area of rectangle = 50

The center of gravity is given by, y = (a

_{1}y

_{1}+ a

_{2}y

_{2}) / (a

_{1}+ a

_{2}) = (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 = (a

_{1}x

_{1}+ a

_{2}x

_{2}) / (a

_{1}+ a

_{2}) = (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)

View Answer

Explanation: Area of triangle = 25, area of rectangle = 100

The center of gravity is given by, y = (a

_{1}y

_{1}+ a

_{2}y

_{2}) / (a

_{1}+ a

_{2}) = (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 = (a

_{1}x

_{1}+ a

_{2}x

_{2}) / (a

_{1}+ a

_{2}) = (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

View Answer

Explanation: The center of gravity is given by, y = (a

_{1}y

_{1}+ a

_{2}y

_{2}+ a

_{3}y

_{3}) / (a

_{1}+ a

_{2}+ a

_{3}) = (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

View Answer

Explanation: The center of gravity is given by, y = (a

_{1}y

_{1}+ a

_{2}y

_{2}) / (a

_{1}+ a

_{2}) = (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

View Answer

Explanation: Area of triangle = 50, area of rectangle = 50

The center of gravity is given by, y = (a

_{1}y

_{1}+ a

_{2}y

_{2}) / (a

_{1}+ a

_{2}) = (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)

View Answer

Explanation: The center of gravity is given by, y = (a

_{1}y

_{1}+ a

_{2}y

_{2}) / (a

_{1}+ a

_{2}) = (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 = (a

_{1}x

_{1}+ a

_{2}x

_{2}) / (a

_{1}+ a

_{2}) = (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

View Answer

Explanation: 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 = (a

_{1}y

_{1}+ a

_{2}y

_{2}+ a

_{3}y

_{3}) / (a

_{1}+ a

_{2}+ a

_{3}) = (16×15 + 24×8 +32×1 / (16 +24+32)) = 6.44cm.

**Sanfoundry Global Education & Learning Series – Strength of Materials. **

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