Correct Answer - Option 2 : (4, 6)
CONCEPT:
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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:
\(x_{com}= {m_1 x_1+m_2 x_2 \over m_1+m_2}\)
\(y_{com}= {m_1 y_1+m_2 y_2 \over m_1+m_2}\)
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) = (0, 0); (x2, y2) = (6, 9) cm; m1 = 1 kg, m2 = 2 kg
Position of the center of mass:
\(x_{com}= {m_1 x_1+m_2 x_2 \over m_1+m_2}={1 \times 0 + 2 \times 6 \over 1+2}=4 \space cm\)
\(y_{com}= {m_1 y_1+m_2 y_2 \over m_1+m_2}={1 \times 0 + 2 \times 9 \over 1+2}=6 \space cm\)
- So the position of the center of mass from the origin will be (4, 6).
- Hence the correct answer is option 2.
