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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 bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is $\frac{\sqrt{x}}{2}$. Then, the value of $x$ is .... .
  • A
    $1$
  • ✓
    $3$
  • C
    $9$
  • D
    $10$
✓

Answer

Correct option: B.
$3$
b
${I}$ in both cases is about point of contact $IAOR,$

Ring,

$m g h=\frac{1}{2} I \omega^{2}$

$m g h=\frac{1}{2}\left(2 m R^{2}\right) \frac{v_{R}^{2}}{R^{2}}$

$V_{R}=\sqrt{g h}$

Solid, cylinder

$m g h=\frac{1}{2} I \omega^{2}$

$m g h=\frac{1}{2}\left(\frac{3}{2} m R^{2}\right) \frac{v_{c}^{2}}{R^{2}}$

$V_{R}=\sqrt{\frac{4 g h}{3}}$

$\frac{v_{R}}{v_{c}}=\frac{\sqrt{3}}{2}$

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