Question

As shown in the figure, a triangular sheet is removed from a uniform rectangular sheet. Then, shift of the centre of mass for the new shape will be:

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 cmCOM of original rectangular sheet will be at O(0,0) Area of rectangular sheet A1=20×60=1200 cm2 Area of triangular part A2=12×20×30=300 cm2 Let the x-coordinates of COM of rectangular shape and triangular shape be x1 and x2 resepctively. Then, x1=0 ∵Position of COM for triangle from it's vertex (O): =23×h=23×30=20 cm ∴x2=(0+20)=20 cm Considering the removed triangular shape as −ve mass superimposed on whole rectangular shape, and applying the formula by considering shapes as point masses at their respective COM, the x-coordinate for COM of remaining part is: xCM=A1x1−A2x2A1−A2 ∴xCM=1200×0−300×201200−300=−6.67 cm Hence, COM of new shape shifts by 6.67 cm along -ve x-axis or leftwards.

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