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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
A solid sphere (mass $2\ M$) and a thin hollow spherical shell (mass $M$) both of the same size, roll down an inclined plane, then
  • ✓
    Solid sphere will reach the bottom first 
  • B
    Hollow spherical shell will reach the bottom first
  • C
    Both will reach at the same time
  • D
    None of these
✓

Answer

Correct option: A.
Solid sphere will reach the bottom first 
a
The rolling sphere with a lower rotational moment of inertia per unit mass than the $2$ cylinders puts less of the potential energy released by falling into rotational kinetic energy and more into linear motion kinetic energy so it falls faster.

It all depends on the moment of inertia. Acceleration is inversely proportional to moment of inertia, as we know that radius and mass of all three is equal and the fact that $M.l.$ is less for sphere. That's why it will reach fastest

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