Two bodies of mass 1 kg and 3 kg have position vectors i ^ + 2 j ^ + k ^ and - 3 i ^ - 2 j ^ + k ^ respectively. The magnitude of position vector of centre of mass of this system will be similar to th

Question

Two bodies of mass 1 kg and 3 kg have position vectors i ^ + 2 j ^ + k ^ and - 3 i ^ - 2 j ^ + k ^ respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector :

TestHub · Accepted Answer

As we know, centre of mass is given by, ${\vec{r}}_{com} = \frac{\sum m_{i} {\vec{r}}_{i}}{\sum m_{i}}$
${\vec{r}}_{com} = \frac{m (\hat{ı} + 2 \hat{ȷ} + \hat{k}) + 3 m (- 3 \hat{ı} - 2 \hat{ȷ} + \hat{k})}{m + 3 m}$
${\vec{r}}_{com} = \frac{- 8 m \hat{ı} - 4 m \hat{ȷ} + 4 m \hat{k}}{4 m} = - 2 \hat{ı} - \hat{ȷ} + \hat{k}$
The magnitude of the position vector of the centre of mass is $\sqrt{2^{2} + 1^{1} + 1^{2}} = \sqrt{6}$ .
It is similar to the magnitude of the option A.

Physics - Center of Mass Question with Solution | TestHub

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