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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))hat(i)`

B

`(-a(5pi -4))/(3(8-pi))hat(i)`

C

`(-a(2pi-4))/(3(8-pi))hat(i)`

D

`(-a(3pi-4))/(2(8-pi))hat(i)`

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) (o i + o hat(j)) + -sigma (pi a^(2))/(2) (a- (4a)/(3pi))hat(i))/(sigma(2a)^(2) - sigma(pi a^(2))/(2)) = (-a(3pi -4))/(3(8-pi)) hat(i)`
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