Question

Two bodies of masses 2 kg and 3
kg are located at (1, 3) and (1, -2)
respectively. The coordinates of
centre of mass will be
(1) O (1,0)
(2) O (0,1)
(3) O (1,1)
(4) None of the above​

Answer 1

Answer:

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Explanation:

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Answer 2

Answer :

Two bodies of masses 2kg and 3kd are located at (1,3) and (1,-2) respectively.

We have to find coordinates of centre of mass.

★ Position of centre of mass of two bodies of masses m₁ and m₂ placed at a distance of r₁ and r₂ from origin is given by

$\dag\:\boxed{\bf{r_{CM}=\dfrac{m_1r_1+m_2r_2}{m_1+m_2}}}$

★ x - coordinate of COM :

$\leadsto\tt\:x_{CM}=\dfrac{m_1x_1+m_2x_2}{m_1+m_2}$

$\leadsto\tt\:x_{CM}=\dfrac{(2)(1)+(3)(1)}{2+3}$

$\leadsto\tt\:x_{CM}=\dfrac{5}{5}$

$\leadsto\bf\:x_{CM}=0$

★ y - coordinate of COM :

$\leadsto\tt\:y_{CM}=\dfrac{m_1y_1+m_2y_2}{m_1+m_2}$

$\leadsto\tt\:y_{CM}=\dfrac{(2)(3)+(3)(-2)}{2+3}$

$\leadsto\tt\:y_{CM}=\dfrac{0}{5}$

$\leadsto\bf\:y_{CM}=0$

$\bigstar\:\boxed{\bf{\purple{(x_{CM},y_{CM})=(1,0)}}}$