Q 2 A semicircular portion of radius r is cut from a uniform rectangle plate as shown in figure - Maths - Limits and Derivatives

Question

Q 2 A semicircular portion of radius r is cut from a uniform
rectangle plate as shown in figure The distance of centre of mass
'c' of remaining plate, from point 'O' is : (A) 2r / 3 - π (b)
3r/2(4- π ) (c) 2r/ (4+ π ) (d) 2r / 3(4- π )

Shobhit Mittal · Accepted Answer

Dear Student,

let the plate density be σCM will shift along x axis X=-πr22σ*-4r3π+2r2σ-r22r
r σ-πr22σ=4r6-r2-π2=2r34-πRegards

Q.2 A semicircular portion of radius r is cut from a uniform rectangle plate as shown in figure . The distance of centre of mass 'c' of remaining plate, from point 'O' is : (A) 2r / 3 - π (b) 3r/2(4- π ) (c) 2r/ (4+ π ) (d) 2r / 3(4- π )

Q.2 A semicircular portion of radius r is cut from a uniform rectangle plate as shown in figure . The distance of centre of mass 'c' of remaining plate, from point 'O' is : (A) 2r / $3 - π$ (b) 3r/2(4- $π$ ) (c) 2r/ (4+ $π$ ) (d) 2r / 3(4- $π$ )