Checkpoint 1 The figure shows a uniform square plate from which four identical s

Question

Checkpoint 1 The figure shows a uniform square plate from which four identical squares at the corners will be removed. (a) Where is the center of mass of the plate originally? Where is it after the removal of (b) square 1 (c) squares 1 and 2; (d) squares 1 and 3; (e) squares 1,2,and 3: (f) all four squares? Answer in terms of quadrants, axes, or points (without calcula tion, of course). Answer: (a) at the origin (b) in Q4, alongy-x (c) along the -y axis (d) at the origin (e) in Q3, along y=x (f) at the origin

Explanation / Answer

a) It is a uniform symmetrical body hence its geometrical centre coincides withe the centre of mass. so the centre of mass situated at the origin

b) here first and third quadrants masses are balanced. mass of the second quadrant is less as compared to the fourth quadrant.Centre of mass is depends on mass and position.It always tends towards higher mass.Hence it is situated at fourth quadrant.

c) Only third and fourth quadrants are here and hence centre of mass is located at the negative y axis.

d) Here are only second and fourth quardrants. Hence the centre of mass is located at the geometrical centre i.e at the origin.

e) Here the mass is concentrated only in third quardant hence the centre of mass is located at the centre of the third quadrant.

f) Again it is a symmetrical body and hence the centre of mass will be located at its geometrical centre i.e at the origin.

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