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  • Try this! - Motion of System Of Particles and Rigid Body - NEET-2

Two bodies of mass 1 kg and 3 kg have position vectors \hat{i}+2\: \hat{j}+\hat{k} and -3\hat{i}-2\: \hat{j}+\hat{k} respectively. The centre of mass of this system has a position vector:

  • Option 1)

    -2 \hat i-2 \hat j+ \hat k]

  • Option 2)

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

  • Option 3)

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

  • Option 4)

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

 

Answers (1)

best_answer

As we learnt in 

Centre of mass when some mass is added in the body -

{vec{r}_{CM}}=frac{m_{1}vec{r_{1}}+{m_{2}}vec{r}_{2}}{m_{1}+m_{2}}

- wherein

m1 &  vec{r_{1}} are mass and position of centre of mass for whole body. m2 & vec{r_{2}} are mass and position of centre of mass of added mass.

 

 

\vec{x}_{c}=\frac{m_{1}\vec{x}_{1}+m_{2}\vec{x}_{2}}{m_{1}+m_{2}}=\frac{1}{4}\left[ -8 \hat i - 4 \hat j - 4 \hat F \right ]

\vec {x}_{c}=-2 \hat i-2 \hat j+ \hat k 


Option 1)

-2 \hat i-2 \hat j+ \hat k]

Correct

Option 2)

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

Incorrect

Option 3)

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

Incorrect

Option 4)

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

Incorrect

Posted by

prateek

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