UNIT-3: Centroids And Centre If Gravity

Question 1

Centroid (of a lamina)

Answer 1

The centre of mass of a geometric object of uniform density

Question 2

Lamina

Answer 2

A uniform thin plate/layer

Question 3

Square

Answer 3

Area = b²
Y = b_y/2
X = b_x/2

Question 4

Rectangle

Answer 4

Area = d*b
Y = d/2
X = b/2

Question 5

Triangle

Answer 5

Area = 1/2bh
Y = h/3
X = it’s on diagonal from apex to b/2

Question 6

Circle

Answer 6

Area = pi*r²
Y = r
X = r

Question 7

Semi-circle

Answer 7

Area = pir²/2 or pid²/8
Y = 4r/3pi
X = 4r/3pi

Question 8

Quarter-circle

Answer 8

Area = pir²/4 or pid²/16
Y = 4r/3pi
X = 4r/3pi

Question 9

Semi-Parabolic Area

Answer 9

Area = 2/2*ab
Y = 3/8 b
X = 2/5 a

Question 10

Centre of gravity (centre of mass)

Answer 10

The point from which the weight of a body/system may be considered to act

Question 11

Rectangular prism

Answer 11

Volume = bdh

Question 12

Triangular prism

Answer 12

Volume = Area of base triangle * h

Question 13

Triangular pyramid

Answer 13

Volume = volume = 1/3 (area of base triangle)(h)

Question 14

Cone

Answer 14

Volume = 1/3 (area of base circle)(h)

Question 15

Cylinder

Answer 15

Volume = area of base circle (h)

Question 16

Sphere

Answer 16

Volume = 4/3pir³ or pi*d³/6

Question 17

Hemisphere

Answer 17

Volume = 2/3 pir³ or pid^3<sup/12