Q.

A circular ring of mass 6 kg and radius a is placed such that its centre lies at the origin. Two particles of masses 2 kg each are placed at the intersecting points of the circle with positive X-axis and positive Y-axis. Then, the angle made by the position vector of centre of mass of entire system with X-axis is

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a

45°

b

60°

c

tan-145

d

30°

answer is A.

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Detailed Solution

P is the position of centre of mass of particles at 2 and 3.Q is position of centre of mass of all three particles.                                 tanθ=yCMxCM=m1y1+m2y2+m3y3m1x1+m2x2+m3x3                                          =6×0+2×0+2×a6×0+2×a+2×0=1 or θ = 45∘
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