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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


  1. 6.67 cm
  2. 4.2 cm
  3. 5.67 cm
  4. 3.2 cm


Solution

The correct option is A 6.67 cm
Let 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=A1r1A2r2A1A2
=1200×0300×201200300
=6.67 cm

Hence, required shift in center of mass is 6.67 cm.

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