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As shown in figure, when a semicircular ...

As shown in figure, when a semicircular cavity is cut from a square plate. Position of com is at

A

`(-a(3pi - 4))/(3(8 - pi)) hati`

B

`(-a(5pi - 4))/(3(8 - pi)) hati`

C

`(-a(2pi - 4))/(3(8 - pi)) hati`

D

`(-a(3pi - 4))/(2(8 - pi)) hati`

Text Solution

Verified by Experts

The correct Answer is:
A
`(m_(1)vec(r_(1)) + m_(2)vec(r_(2)))/(m_(1) + m_(2)) = vec(r_(com))`
`vec(r_(com)) = (sigma (2a^(2))(oi + ohatj) -sigma(pia^(2))/(2) (a - (4a)/(3pi))hati)/(sigma(2a)^(2) - sigma(pia^(2))/(2)) = (-a(3pi - 4))/(3(8 - pi))hat i`
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