Question

Two bodies of masses 10kg and 20kg are located in xy plane at (0,1) and (1,0). Find the position of centre of mass.

Answer 1

Answer:

1,1

Explanation:

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Answer 2

Answer:

The position of centre of mass is $\big(\frac{2}{3} ,\frac{1}{3}\big)$.

Explanation:

Given the masses of two bodies, $m_{1} = 10kg$ and $m_{2} = 20kg$

Location of masses in xy plane is at (0,1) and (1,0)

Thus the x - coordinates are  $x_{1} = 0$ and $x_{2} = 1$

And similarly y - coordinates are  $y_{1} = 1$ and $y_{2} = 0$

The center of mass is defined as the average position of all the elements of the system, weighted according to their masses.

For a system of two masses  $m_{1}$ and $m_{2}$, the position of center of mass with respect to x and y coordinates is given by

$x_{com} =\frac{m_{1}x_{1} +m_{2}x_{2} }{m_{1}+m_{2}}$ and $y_{com} =\frac{m_{1}y_{1} +m_{2}y_{2} }{m_{1}+m_{2}}$

Thus,

$x_{com} =\frac{10\times 0+20\times 1}{10+20}=\frac{20}{30} =\frac{2}{3}$

$y_{com} =\frac{10\times 1+20\times 0}{10+20}=\frac{10}{30} =\frac{1}{3}$

Hence, the position of centre of mass is $\big(\frac{2}{3} ,\frac{1}{3}\big)$.