Skip to content
doubtly
Sign up
Log in to upvote 0 Log in to downvote
Chapter: Centroid· Engineering Mechanics

Find the coordinates of the centroid of the shaded lamina with respect to the given reference axes.Figure (described in words): Origin O at the bottom-left corner, x-axis to the right, y-axis upward; dimensions in cm. The lamina is made of: a rectang…

Q.5 Find the coordinates of the centroid of the shaded lamina with respect to the given reference axes.

Figure (described in words): Origin O at the bottom-left corner, x-axis to the right, y-axis upward; dimensions in cm. The lamina is made of: a rectangle with corners (0, 0), (8, 0), (8, 6) and (0, 6); a semicircle of radius 4 cm standing on the top edge of the rectangle (diameter from (0, 6) to (8, 6), curved side upward); and a right-angled triangle on the right side with vertices (8, 0), (12, 0) and (8, 6). A circular hole of diameter 3 cm centred at (4, 3) is cut out. The rest is shaded.

Doubtly AI Asked AI-generated · not yet verified Practice test mu engineering Save WhatsApp Report
Sign in to comment

1 answer

Log in to upvote 0 Log in to downvote

Best answer

Answer: \(\bar x=4.82\) cm, \(\bar y=4.36\) cm.

PartArea \(A\) (cm²)\(x\) (cm)\(y\) (cm)\(Ax\)\(Ay\)
1. Rectangle 8 × 64843192144
2. Semicircle, \(r=4\)\(\frac{\pi(4)^2}{2}=25.13\)4\(6+\frac{4r}{3\pi}=7.698\)100.53193.46
3. Triangle\(\frac12(4)(6)=12\)\(8+\frac43=9.333\)\(\frac63=2\)11224
4. Hole, \(r=1.5\) (subtract)\(-\pi(1.5)^2=-7.07\)43−28.27−21.21
Total78.06376.26340.25

Notes: the centroid of a semicircle lies \(\frac{4r}{3\pi}=\frac{16}{3\pi}=1.698\) cm from its diameter; the centroid of the right triangle with vertices (8, 0), (12, 0), (8, 6) is at the average of the vertices, \(\left(\frac{8+12+8}{3},\frac{0+0+6}{3}\right)=(9.333,2)\).

\[\bar x=\frac{\sum Ax}{\sum A}=\frac{376.26}{78.06}=4.82\ \text{cm},\qquad\bar y=\frac{\sum Ay}{\sum A}=\frac{340.25}{78.06}=4.36\ \text{cm}\]

Doubtly AI · 27 Oct 2026 AI-verified · Oct 2026 Report
Was this answer helpful?
Sign in to comment

Your answer

Log in or create a free account to answer this question.