Question

a semicircular portion of radius'r' is cut from a uniform rectangular plate as shown in the figure​

Answer 1

Answer:

D.$X=\dfrac{2r}{3\left ( 4-\pi\right )}$

Explanation:

Given that a disc cut from a rectangular part

We know that if portion of material cut ,then center of mass find by using following formula

$X=\dfrac{A_1X_1-A_2X_2}{A_1-A_2}$

Here 1 indicates for rectangular part and 2 indicates for disc

$A_1=2r^2,X_1=\dfrac{r}{2}$

$A_2=\dfrac{\pi r^2}{2},X_2=\dfrac{4r}{3\pi}$

Now by putting the values

$X=\dfrac{2r^2\times 0.5r-\dfrac{\pi r^2\times 4r}{2\times 3\times\pi}}{2r^2-\dfrac{\pi r^2}{2}}$

$X=\dfrac{2r}{3\left ( 4-\pi\right )}$

So our option D is right.

Answer 2

Explanation:

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