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NEET 2009
Exam
NEET
Year
2009
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

NEET 2009 · Physics · Center of Mass, Momentum and Collision

Two bodies of mass 1 ~kg and 3 ~kg have position vectors i +2 j + k...

Two bodies of mass 1 kg1 \mathrm{~kg} and 3 kg3 \mathrm{~kg} have position vectors i^+2j^+k^\hat{i}+2 \hat{j}+\hat{k} and −3i^−2j^+k^-3 \hat{i}-2 \hat{j}+\hat{k}, respectively. The centre of mass of this system has a position vector

Options

  1. A−2i^+2k^-2 \hat{i}+2 \hat{k}
  2. B−2i^−j^+k^-2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}
  3. C2i^−j^−2k^2 \hat{i}-\hat{j}-2 \hat{k}
  4. D−i^+j^+k^-\hat{i}+\hat{j}+\hat{k}

Correct answer

B. −2i^−j^+k^-2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}

Step-by-step solution

The position vector of centre of mass r⃗=m1r1→+m2r⃗2m1+m2=1(i^+2j^+k^)+3(−3i^−2j^+k^)1+3=14(−8i^−4j^+4k^)=−2i^−j^+k^\begin{aligned} \vec{r}& =\frac{m_1 \overrightarrow{r_1}+m_2 \vec{r}_2}{m_1+m_2}\\ & =\frac{1(\hat{i}+2 \hat{j}+\hat{k})+3(-3 \hat{i}-2 \hat{j}+\hat{k})}{1+3}\\ & =\frac{1}{4}(-8 \hat{i}-4 \hat{j}+4 \hat{k}) \\ & =-2 \hat{i}-\hat{j}+\hat{k} \end{aligned}The centre of mass changes its position only under the translatory motion. There is no effect of rotatory motion on centre of mass of the body.
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