question_answer

Pour point masses P, Q, R and S with respective masses 1 kg, 1 kg, 2 kg and 2 kg form the comers of a square of side a. The centre of mass of the system will be farthest from

A)  P only                                  

B)  R and S

C)  R only                                  

D)  P and Q

E)  P and R

Correct Answer: D

Solution :

                Centre of mass \[{{C}_{1}}\] of the point masses placed at comers P and S from point P \[=\frac{1\times 0+2\times a}{1+2}=\frac{2a}{3}\] Therefore, distance of centre of mass \[{{C}_{1}}\] from point S \[=a-\frac{2a}{3}=\frac{a}{3}\] Similarly centre of mass \[{{C}_{2}}\]of point masses placed at comers Q and R, from point\[Q=\frac{2a}{3}\] Distance of centre of mass \[{{C}_{2}}\] from point R \[=a-\frac{2a}{3}=\frac{a}{3}\] Centre of mass of all four point masses is at the mid point of the line joining \[{{C}_{1}}\] and \[{{C}_{2}},\] which is farthest from points P and Q.