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

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics6. system of particles and rotational motion1 Mark
MCQ
Two uniform solid spheres having unequal masses and unequal radii are released from rest from the same height on a rough incline. If the spheres roll without slipping,
  • A
    the heavier sphere reaches the bottom first
  • B
    the bigger sphere reaches the bottom first
  • ✓
    the two spheres reach the bottom together
  • D
    the information given is not sufficient to tell which sphere will reach the bottom first.
✓

Answer

Correct option: C.
the two spheres reach the bottom together
c
(c)

Since acceleration of a body during rolling without slipping, on an inclined plane of angle $\theta$ is given by

$a=\frac{g \sin \theta}{1+\frac{K^2}{R^2}}$, where $K$ is radius of gyration.

For solid sphere, $\frac{ K ^2}{ R ^2}=\frac{2}{5}$

Thus, $a=\frac{5}{7} g \sin \theta$

So, acceleration is independent of both mass and radius. Both spheres will reach bottom together.

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