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In the figure shown a semicircular area is removed from a uniform square plate of side `l` and mass ‘m’ (before removing). The x-coordinate of centre of mass of remaining portion is (The origin is at the centre of square) A. `-(pi(pi-2)l)/(2(8-pi))`B. `(pi(pi-2)l)/(2(8-pi))`C. `-(pi(pi-2)l)/(8-pi)`D. `-(l(pi-4/3))/(2(8-pi))` |
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Answer» `x_(cm)=(m_(1)x_(1)+m_(2)x_(2))/(m_(1)+m_(2))` `m_(1)`=mass of square plate `=m` `x_(1)`=c.m. of square plate =0 `m_(2)` =mass of removed part `=-m/(l^(2))((pi(l^(2))/4)/2)=-(pi)/8 m` `x_(2)`=c.m. of removed part `=l/2-4/(3pi)(l/2)=l/2(1-4/(3pi))` `:. x_(cm)=(-(pim)/8.l/2(1-4/(3pi)))/(m-(pi)/8m), x_(cm)=-(l(pi-4/3))/(2(8-pi))` |
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