Explanation Given information: The Equation of curve ( y ) is y = r = k x n Calculation: Express the Equation of curve ( y ) as shown below: y = r = k x n (1) For x = h , r = a Find the constant factor ( k ) as shown below: Substitute a for r and h for x in Equation (1). a = k h n k = a h n Substitute a h n for k in Equation (1). r = ( a h n ) x n Sketch the revolving element as shown in Figure 1. Find the differential element of mass ( d m ) as shown below: m = ρ V (2) Here, ρ is density and V is volume of cylinder. Differentiate Equation (2) with respect to V . d m = ρ d V (3) Substitute π r 2 d x for d V in Equation (3). d m = ρ ( π r 2 d x ) Find the strip element ( d I x ) about x axis as shown below: d I x = 1 2 r 2 d m Express the mass moment of inertia of the solid with respect to x axis in terms of m and h by using direct integration. I x = ∫ d I x = ∫ 1 2 r 2 d m = 1 2 ∫ 0 h r 2 ( ρ π r 2 d x ) = 1 2 ρ π ∫ 0 h r 4 d x = 1 2 ρ π ∫ 0 h ( a h n x n ) 4 d x = 1 2 ρ π a 4 h 4 n ∫ 0 h x 4

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Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provi…

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Chapter 9.5, Problem 9.121P

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Express the mass moment of inertia of the solid with respect to x axis in terms of m and h by using direct integration.

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Chapter 9.5, Problem 9.120P

Chapter 9.5, Problem 9.122P

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Express the mass moment of inertia of the solid with respect to x axis in terms of m and h by using direct integration.

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Express the mass moment of inertia of the solid with respect to x axis in terms of m and h by using direct integration.

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