Grade 11Mechanics
FIND THE CENTER OF MASS OF A UNIFORM PLATE HAVING SEMICIRCULAR INNER AND OUTER BOUNDARIES OF RADII R1 AND R2
FIND THE CENTER OF MASS OF A UNIFORM PLATE HAVING SEMICIRCULAR INNER AND OUTER BOUNDARIES OF RADII R1 AND R2
1 Answer
Subrata Dutta
Let , a small part of the plate of breadth ‘dx’ , at a distance x(variable) from the centre. Area of this part= pi xdx and mass of this part , dm =2 (M× pi xdx)/ pi(R22 - R21) = 2Mxdx/(R22 – R21) . Also the small part which we have drawn is similar to a wire , whose c.m is at 2x/pi from the centre. So , if the c.m of the given plate is at y from centre then, M×y = R1∫R2 dm× 2x/pi = 4(R21 +R1R2+R22)/3pi(R1+R2) above the centre.(ans)
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