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

Options

A. `1/3(hat(i)-hat(j))`
B. `2/3(hat(i)-hat(j))`
C. `2/3(hat(i)+hat(j))`
D. `1/3(hat(i)+hat(j))`

Answer

C

Explanation

`x_(CM)=(summ_(1)x_(1))/(summ_(1))=(m times 0+ m times 0+m times 2)/(m+m+m)=2/3`
`y_(CM)=(summ_(1)y_(1))/(summ_(1))=(m times 2+m times 0+ m times 0)/(m+m+m)=2/3" "therefore" Position vector of centre of mass is "2/3(hat(i)+hat(j))`