A disk and a sphere of same radius but different masses roll off on...

A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

Options

ADisk
BSphere
CBoth reach at the same time
DDepends on their masses

Correct answer

B. Sphere

Step-by-step solution

Acceleration of the object on rough inclined plane is

\text{a} = \dfrac{\text{g}sin\text{\theta}}{1 + \dfrac{\text{I}}{{\text{mR}}^{2}}} = \dfrac{gsin\theta}{1 + \dfrac{{K}^{2}}{{R}^{2}}}

For sphere

{\text{a}}_{1} = \dfrac{5\text{g}sin\text{\theta}}{7} ( \dfrac{{K}^{2}}{{R}^{2}} = \dfrac{2}{5} )

For disc

{\text{a}}_{2} = \dfrac{2\text{g}sin\text{\theta}}{3} ( \dfrac{{K}^{2}}{{R}^{2}} = \dfrac{1}{2} )

{a}_{1} > {a}_{2}

, so sphere will reach bottom first.

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