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Question

# As shown in the figure, from a uniform rectangular sheet, a triangular sheet is removed from one edge. The shift of the centre of mass (with respect to O) is

A
3.2 cm
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B
4.2 cm
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C
5.67 cm
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D
6.67 cm
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Solution

## The correct option is D 6.67 cmLet A1 be the area of rectangle and A2 be the mass of triangle removed. By the symmetry. Ycom will be zero. A2=(12×30×20)=300 A1=20×60=1200 Taking origin at O, Position of centre of mass of rectangle r1=0 Position of center of mass of triangle (r2)=23×height =23×30=20 cm Now. Xcom=A1r1−A2r2A1−A2 =1200×0−300×201200−300 =−6.67 cm Hence, required shift in center of mass is 6.67 cm.

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