Two masses are placed in x-y plane. 1 kg mass is at (6, 6) and 2 kg is placed at (x, y). Find the value of (x, y) if the centre of mass of two masses is at origin.

CONCEPT:

• Center of mass: Centre of the mass of a body is a point at which the whole of the mass of the body appeared to be concentrated.
• The position of the center of mass of a three-body system in the x-direction is calculated by:

where xcom is the position of the center of mass in x-coordinate, ycom is the position of the center of mass in y-coordinate, m1, m2, and m3 are the masses of three bodies, x1, x2, and x3 are the position of different masses in x-coordinate, y1, y2, and y3 are the position of different masses in y-coordinate.

CALCULATION:

Given that (x1,y1) = (6, 6); (x2,y2) = (x, y) cm; m1 = 1 kg, m2 = 2 kg;  (xcom,ycom) = (0, 0) 

• Position of the center of mass in x - axis:

⇒ x = - 3

Position of the center of mass in x - axis

⇒ y = - 3

• So the position of 2^nd mass will be (x, y) = (-3, -3). Hence the correct answer is option 3.