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The figure shows a uniform semi-circular metal plate of radius ‘r’ obtained by cutting a circular plate across a diameter. The distance ‘x’ between the center of mass of the plate from the center of the original circular plate is

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$4r/3π$

r/2

2r/3

3r/4

answer is B.

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Detailed Solution

According to Pappu's theorem

V = A x l $\to$ $\frac{4}{3} π r^{3} = \frac{π r^{2}}{2} \times 2 π X_{c}$

where l is the distance moved by COM on a full rotation and A is the area of plate

$X_{c} = \frac{4 r}{3 π}$

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