Question

Module 8 6 4 Determine the centroid of the area shown when a = 10 in. 뾔 12.5 points Hinz in

Answer 1

Given that, Area a = 10 in The schematic diagram of the area is, Now we are consider the elemental area of width dx \r\n Now calculate the centroid of the entire area consider the entire area (1) to be square of the side a and then subtracting the area The equation of the curve is Y = 1/x The limits are, y = a x = 1/a Now, the differential element of area is dA integral dA = integral_a^1/a (y - a) dx \r\n Substitute the above y values in equation = integral_a^1/a (1/x - a) dx Integrating the above relation, A_2 = (ln (x) - ax)_a^1/a Substitute the limits, we get A_2 = (ln (1/a) - a(1/a)) - (ln (a) - a^2) = -ln (a) - 1 - ln (a) + a^2 A_2 = a^2 - 2 ln - 1 The differential element with respect to y-axis is X_el^- dA for the first moment of area. The total area with