Three identical spheres , each of mass M , are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 2 m . Taking their point of intersection as the origin , find the position vector of centre of mass

Explanation

`x = (m_(1) x_(1) + m_(2) x_(2) + m_(3) x_(3))/(m_(1) + m_(2) + m_(3))`
`therefore = ((M xx 0) + (M xx 0) + (M xx 2))/(M + M + M) = (2M)/(3 M) = (2)/(3) m`

`therefore` x-coordination = `2//3 hati`
Again `y = ((M xx 2) + ( M xx 0) + ( M xx 0))/(M + M + M)`
or `y = (2M)/(3M) = (2)/(3)` m
`therefore` y-coordinate = `2//3 hatj`
`therefore` Position vector of centre of mass = `(2)/(3) hati + (2)/(3) hatj = (2)/(3) (hati + hatj)`