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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 cm
COM 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=A1x1A2x2A1A2

xCM=1200×0300×201200300=6.67 cm

Hence, COM of new shape shifts by 6.67 cm along -ve x-axis or leftwards.

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