Question

the mass of the moon is 0.0123 tomes the mass of the earth and separation between them is 3.84×10^8meters determine the location of centre of mass as measured from the centre of the earth ​

Answer 1

Explanation:

Let M be the mass of the Earth

Then 0•0123M Is the mass of the Moon

if r be distance of the C.M of the Earth-Moon system

then

Mr = 0•0123

Answer 2

The center of mass  is $4.66\times10^{6}\ m$

Explanation:

Given that,

Mass of moon $M_{m}= 0.0123M_{e}$

Separation $d=3.84\times10^{8}\ m$

We need to calculate the center of mass

Using formula of center of mass

$x_{cm}=\dfrac{m_{1}x_{1}+m_{2}x_{2}}{m_{1}+m_{2}}$

Put the value into the formula

$x_{cm}=\dfrac{M_{e}\times0+0.0123M_{e}\times3.84\times10^{8}}{M_{e}+0.0123M_{e}}$

$x_{cm}=\dfrac{M_{e}(4723200)}{M_{e}(1.0123)}$

$x_{cm}=4665810.53\ m$

$x_{cm}=4.66\times10^{6}\ m$

Hence, The center of mass  is $4.66\times10^{6}\ m$

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Topic : center of mass

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