A circular ring of mass 6kg and radius a is placed such that its center of 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 center of mass of entire system with X-axis is

Options

A. `45^(@)`
B. `60^(@)`
C. `tan ^(-)(4/5)`
D. `30^(@)`

Answer

A

Explanation

P is the position of center of mass of particle at 2 and 3. Q is position of center of mass of all three particles.

`tantheta = y_(CM)/x_(CM) = ((m_(1)y_(1)+m_(2)y_(2)+m_(3)y_(3))/(m_(1)x_(1)+m_(2)y_(2)+m_(3)y_(3))`
`( 6 xx0+2xx0+2xxa)/(6xx0+2xxa+2xx0) = 1`
or `theta = 45^(@)`