Two uniform solid spheres having unequal masses and unequal radii… - Vidyadip

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:
$\text{a}=\frac{\text{g}\sin\theta}{1+\frac{\text{I}_{\text{COM}}}{\text{mr}^2}}$
$I_\text{COM}$ 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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