Two particles of masses 1 kg and 2 kg are positioned on x-and y-axes at distances of 1 m and 2 m from the origin respectively. Find the position of the centre of mass of the system.

Explanation

Mass of first particle `m_(1)` =1 kg and its position is (1,0). Mass of second particle is `m_(2)` = 2 kg and it is positioned at `(0,2)`.
Let the coordinates of the centre of mass of the system be `(x_("cm"),y_("cm"))`.
`:." "x_("cm")=(m_(1)x_(1)+m_(2)x_(2))/(m_(1)+m_(2))=(1xx1+2xx0)/(1+2)=(1)/(3)`m
and `y_("cm")=(m_(1)y_(1)+m_(2)y_(2))/(m_(1)+m_(2))=(1xx0+2xx2)/(1+2)=(4)/(3)`m
Hence, the distance of the centre of mass from the 1 kg mass `=sqrt((1-(1)/(3))^(2)+(0-(4)/(3))^(2))=(2sqrt(5))/(3)` m and that from the 2 kg mass `=sqrt((0-(1)/(3))^(2)+(2-(4)/(3))^(2))=(sqrt(5))/(3)`m.