Centroids and Moments of Inertia: Master Engineering Mechanics with Confidence

Question 1

Find the centroid of a triangle with vertices (0,0), (a,0), and (0,b).

Accepted Answer

(a/3, b/3)

Answer

(2a/3, 2b/3)

Answer

(a/2, b/2)

Answer

(a/4, b/4)

Question 2

Provide the formula for the centroid of a semi-circular area of radius 'r'.

Accepted Answer

(4r/3π, 0)

Answer

(2r/3π, 0)

Answer

(3r/4π, 0)

Answer

(r/2, r/2)

Question 3

Calculate the moment of inertia of a circular area of radius 'r' about an axis perpendicular to its plane and passing through its centre.

Accepted Answer

πr^4/4

Answer

πr^4/2

Answer

πr^4

Answer

2πr^4

Question 4

Calculate the centroid of a triangular area with base 'b' and height 'h':

Accepted Answer

b/2, h/3

Answer

b/3, h/2

Answer

b/4, h/3

Answer

b/3, h/4

Question 5

In the context of centroids, the first moment of an area about an axis is known as:

Accepted Answer

Centroidal Distance

Answer

Moment of Inertia

Answer

Area Moment

Answer

Geometric Moment

Question 6

The centroid of a triangle lies at the intersection of its:

Accepted Answer

Medians

Answer

Bisectors

Answer

Altitudes

Answer

Axes of Symmetry

Question 7

The moment of inertia of a composite area is equal to the sum of the moments of inertia of its:

Accepted Answer

Individual components

Answer

Centroidal distances

Answer

Cross-sectional areas

Answer

Material densities

Question 8

In the context of area moments of inertia, the product of an area element and the square of its distance from an axis is known as:

Accepted Answer

Second Moment of Area

Answer

First Moment of Area

Answer

Area Moment

Answer

Mass Moment of Inertia

Question 9

The polar moment of inertia of a circular cross-section with radius 'r' is given by:

Accepted Answer

(πr^4)/2

Answer

(πr^2)/4

Answer

2πr^3

Answer

πr^2

Question 10

Calculate the moment of inertia about the x-axis for the rectangular area with width 'b' and height 'h'.

Accepted Answer

(bh³/12)

Answer

(2bh³)

Answer

(bh³)

Answer

(bh³/6)

Question 11

Determine the moment of inertia about the x-axis for the semi-circular area with radius 'r'.

Accepted Answer

(πr⁴)/8

Answer

(πr²)/8

Answer

(πr³)/8

Answer

(2πr⁴)/8

Question 12

Which of the following statements accurately describes the parallel axis theorem for moments of inertia?

Accepted Answer

The moment of inertia of a body about any axis parallel to its centroidal axis is equal to the moment of inertia about the centroidal axis plus the product of the mass and the square of the distance between the two axes.

Answer

The moment of inertia of a body about its centroidal axis is always minimum.

Question 13

Which of the following correctly defines the radius of gyration?

Accepted Answer

The distance from the centroid of an area or a body to an axis of rotation such that the moment of inertia about that axis is equal to the mass or area times the square of the radius of gyration.

Answer

The distance from the centroid of an area or a body to the axis of rotation about which the moment of inertia is maximum.

Question 14

Which of the following statements about moments of inertia is true?

Accepted Answer

The moment of inertia of a body about an axis perpendicular to a plane of symmetry is equal to the sum of the moments of inertia about two perpendicular axes in the plane of symmetry.

Answer

The moment of inertia of a body about any axis is always maximum.

Question 15

The centroid of a triangular area with base b and height h is located at a distance of:

Accepted Answer

b/3 from the base

Answer

b from the base

Answer

b/4 from the base

Answer

b/2 from the base

Question 16

The parallel axis theorem states that the moment of inertia of an area about an axis parallel to and at a distance d from its centroidal axis is:

Accepted Answer

I = I_c + Ad^2

Answer

I = I_c - Ad^2

Answer

I = 2I_c + Ad^2

Answer

I = I_c/Ad^2

Question 17

The perpendicular axis theorem states that the moment of inertia of an area about an axis perpendicular to its plane is equal to the sum of the moments of inertia about two perpendicular centroidal axes in the plane.

Accepted Answer

True

Answer

Not enough information provided

Answer

False

Answer

Sometimes true, sometimes false