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STD 11 - 6. system of particles and rotational motion — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 6. system of particles and rotational motion4 Marks
MCQ
Two semicircular rings of linear mass densities $\lambda $ and $3\lambda $ and of radius $R$ each are joining to form a complete ring. The distance of the centre of the mass of complete ring from its geometrical centre is
  • A
    $\frac{{2R}}{{3\pi }}$
  • ✓
    $\frac {R}{\pi }$
  • C
    $\frac{{2R}}{{\pi }}$
  • D
    $\frac{R}{{3\pi }}$
✓

Answer

Correct option: B.
$\frac {R}{\pi }$
b
Let the mass of ring having density $\lambda$ be $M.$

Centre of mass

$\frac{M_{1} x_{1}+M_{2} x_{2}}{M_{1}+M_{2}}=\frac{-M \frac{2 R}{\pi}+3 M \cdot \frac{2 R}{\pi}}{4 M}=\frac{R}{\pi}$

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