Question

Two bodies of masses 1 kg and 2 kg are lying in xy
plane at (-1, 2) and (2, 4) respectively. What are
coordinates of COM?​

Answer 1

Answer:

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Answer 2

SoluTion:

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Let the coordinates of centre of mass be (x, y).

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We know that,

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$\sf{x_{CM} = \dfrac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}}$

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Here,

• $\sf{m_{1} = 1\:kg}$

• $\sf{x_{1} = -1}$

• $\sf{m_{2} = 2\:kg}$

• $\sf{x_{2} = 2}$

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†Putting the values,

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$\longrightarrow$ $\sf{x_{CM} = \dfrac{1 \times (-1) + 2 \times 2}{1+2}}$

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$\longrightarrow$ $\sf{x_{CM} = \dfrac{-1+4}{3}}$

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$\longrightarrow$ $\sf{x_{CM} = \dfrac{3}{3}}$

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$\longrightarrow$ $\sf{x_{CM} = 1}$

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Similarly,

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$\sf{y_{CM} = \dfrac{m_{1} y_{1} + m_{2} y_{2}}{m_{1} + m_{2}}}$

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Here,

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• $\sf{m_{1} = 1\:kg}$

• $\sf{y_{1} = 2}$

• $\sf{m_{2} = 2\:kg}$

• $\sf{y_{2} = 4}$

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†Putting the values,

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$\longrightarrow$ $\sf{y_{CM} = \dfrac{1 \times (2) + 2 \times 4}{1+2}}$

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$\longrightarrow$ $\sf{y_{CM} = \dfrac{2+8}{3}}$

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$\longrightarrow$ $\sf{y_{CM} = \dfrac{10}{3}}$

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$\therefore$ $\sf{Coordinates\:of\:centre\:of\:mass\:will\:be\:\bigg( 1, \dfrac{10}{3} \bigg)}$