Q64 / 120 · NEET 2010 (Mains) · Physics

The solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on a inclined plane. Both roll down without slipping. Which one will reach the bottom first?

  • A
    Both together only when angle of inclination of plane is $45^{\circ}$
  • Correct answer
    B
    Both together
  • C
    Hollow cylinder
  • D
    Solid cylinder

Solution

$\mathrm{t}=\frac{1}{\sin \theta} \sqrt{\frac{2 \mathrm{~h}}{\mathrm{~g}}\left(1+\frac{\mathrm{k}^2}{\mathrm{R}^2}\right)}$ If a solid and hollow body of same shape are allowed to roll down on inclined plane then as $\left(\frac{\mathrm{k}^2}{\mathrm{R}^2}\right)_{\mathrm{S}} < \left(\frac{\mathrm{k}^2}{\mathrm{R}^2}\right)_{\mathrm{H}}$, solid body will reach the bottom first with greater velocity.

Hence, the correct answer is option: 'B'.

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