(a) Explanation The diagram for the centre of gravity is depicted below: Refer fig 1. Write the equation of centre of gravity along y-direction, Y ¯ Σ A = Σ y ¯ A (I) Here, the centre of gravity along y-axis is Y ¯ , the length is Σ A , the area is Σ y ¯ A . Conclusion: Substitute [ b a ( a − k h ) ] for Σ A , b 6 ( a 2 − k h 2 ) for Σ y ¯ A in Equation (I). Y ¯ [ b a ( a − k h ) ] = b 6 ( a 2 − k h 2 ) Y ¯ = a 2 − k h 2 3 ( a − k h ) (II) For maximum value, d Y ¯ d h = 0 (III) Substitute, ( a 2 − k h 2 3 ( a − k h ) ) for Y ¯ in equation (III), d [ ( a 2 − k h 2 3 ( a − k h ) ) ] (b) To determine The distance ( h ) for which the centroid of the shaded area when ( k = 0.80 ) .

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Center of Gravity and Centroid

The term center of gravity indicates the position or location of a point about which the whole weight of a body or system is supposed to be concentrated, which means the whole weight of the body or system works through this point. It is closely related t…

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Chapter 5.1, Problem 5.32P

(a)

To determine

The distance (h) for which the centroid of the shaded area when (k=0.10).

(b)

To determine

The distance (h) for which the centroid of the shaded area when (k=0.80).

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Chapter 5.1, Problem 5.31P

Chapter 5.1, Problem 5.33P

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The distance ( h ) for which the centroid of the shaded area when ( k = 0.10 ) .

Solution Summary: The diagram for the centre of gravity is depicted below.