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

Option: 1

\begin{aligned} &\hat{i}+2 \hat{j}+\hat{k} \\ \end{aligned}


Option: 2

\mathrm{-3 \hat{i}-2 \hat{j}+\hat{k} }
 


Option: 3

\mathrm{-2 \hat{i}+2 \hat{k} }
 


Option: 4

\mathrm{-2 \hat{i}-\hat{j}+2 \hat{k}}


Answers (1)

best_answer

\mathrm{\bar{r}_1 =\hat{i}+2 \hat{\jmath}+\hat{k} }

\mathrm{\bar{r}_2 =-3 \hat{i}-2 \hat{\jmath}+\hat{k} }

\mathrm{\bar{r}_{\text {com }} =\frac{m_1 \bar{r}_1+m_2 \bar{r}_2}{m_1+m_2} }

          \mathrm{=\frac{(\hat{i}+2 \hat{\jmath}+\hat{k})+3(-3 \hat{i}-2 \hat{j}+\hat{k})}{4} }

          \mathrm{=\frac{-8 \hat{i}-4 \hat{\jmath}+4 \hat{k}}{4} }

\mathrm{\bar{r}_{\text {com }} =-2 \hat{i}-\hat{\jmath}+\hat{k} }

\mathrm{\left|\bar{r}_{\text {com }}\right| =\sqrt{4+1+1}=\sqrt{6} }

The magnitude of position vector of centre of mass of this system \mathrm{\left|\bar{r}_{\text {com }}\right|=\sqrt{6}} is similar to the magnitude of vector \mathrm{(\hat{i}+2 \hat{j}+\hat{k})}

Hence 1 is correct option.

Posted by

shivangi.shekhar

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