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Rotational Mechanics — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsRotational Mechanics1 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.
Acceleration of a sphere on the incline plane is given by:
$\text{a}=\frac{\text{g}\sin\theta}{1+\frac{\text{I}_{\text{COM}}}{\text{mr}^2}}$
$\mathrm{I}_{\mathrm{COM}}$ for a solid sphere $=\frac{2}{5}\text{mr}^2$
So, $\text{a}=\frac{\text{g}\sin\theta}{1+\frac{2\text{mr}^2}{5\text{mr}^2}}=\frac{5}{7}\text{g}\sin\theta$
a is independent of mass and radii; therefore, the two spheres reach the bottom together.

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