Worksheets17/12 AE
Total questions: 10
Worksheet time: 5mins
A semicircle of radius 9 cm is oriented with its flat diametral base along the x-axis. What is the y-coordinate of its centroid?
3 cm
4 cm
12/π cm
9/π cm
Analyze the following statements regarding the fundamental differences between Centroid and Centre of Gravity (COG).
• Statement I: The Centroid is a purely geometric property of an area, independent of material density. • Statement II: The Centre of Gravity depends on both the shape and the density distribution of a body. • Statement III: For a 3D object of uniform density, its Centroid and Centre of Gravity coincide. Which of the above statements is/are correct?
Statement I only
Statements I and II only
Statements II and III only
All statements I, II, and III are correct.
Select the single best answer. Varignon’s Theorem, also known as the Principle of Moments of Components, states that:
For a body in equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments.
A couple produces a pure rotational effect with zero resultant force.
The moment of a force about a point is equal to the algebraic sum of the moments of its orthogonal components about the same point.
The centroid of a composite area is the weighted average of the centroids of its component parts.
Select the single best answer. In beam analysis, the centroid of the cross-sectional area is crucial for locating which important feature?
The point of maximum shear stress.
The neutral axis.
The outer fiber of the beam.
The point of load application.
For a physical body with varying density, such as a hammer with a heavy steel head and a light wooden handle, how does the Centre of Gravity (COG) relate to the geometric Centroid?
The COG and Centroid will still coincide perfectly.
The COG is shifted from the Centroid towards the lighter region (the wooden handle).
The COG is shifted from the Centroid towards the heavier region (the steel head).
The concept of a Centroid does not apply to 3D objects like a hammer.
Evaluate the following technical statements regarding fundamental concepts in mechanics.
• Statement I: The Moment of Inertia (MOI) is defined as the second moment of area and can have a positive or negative value.
• Statement II: A force applied directly through a body's Centre of Gravity (CG) will produce only a translational effect, with no rotational effect. Which statement(s) is/are true?
Statement I only
Statement II only
Both Statement I and Statement II are true.
Neither Statement I nor Statement II is true.
Select the single best answer. A quarter circle of radius 'r' is placed with its straight edges along the positive x and y axes. The coordinates of its centroid (xˉ,yˉ) are:
(r/2,r/2)
(r/3,r/3)
(4r/3π,4r/3π)
(3r/4π,3r/4π)
Select the single best answer. A composite section is made of multiple simple shapes. The formula xˉ=(∑Ai×xi)/(∑Ai) represents:
Varignon's Theorem for finding a resultant moment.
The law of moments for establishing equilibrium.
The area-moment method for locating the x-coordinate of the composite centroid.
The formula for calculating the moment of a couple.
Select the single best answer. Consider a rectangle with base 'b' and depth 'd'. A hollow concentric rectangle with dimensions 'b_inner' and 'd_inner' is removed from it. Where is the centroid of the resulting hollow rectangular section?
At the centroid of the inner removed rectangle.
Shifted towards the thicker part of the section.
At the geometric center, coinciding with the centroid of the original rectangle.
It cannot be determined without knowing the areas.
Select the single best answer. A force is applied to a rigid body. Under which condition will this force produce a pure translational effect with no rotation?
When the force is applied perpendicular to the body's main axis.
When the line of action of the force passes through the body's Centre of Gravity (CG).
When the force is part of a couple.
When the force is applied at the point furthest from the CG.
