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?

Question

Aicharya · Accepted Answer

Acceleration of the object on rough inclined plane is

a = \frac{g \sin θ}{1 + \frac{I}{{mR}^{2}}} = \frac{g \sin θ}{1 + \frac{K^{2}}{R^{2}}}

For sphere

a_{1} = \frac{5 g \sin θ}{7} (\frac{K^{2}}{R^{2}} = \frac{2}{5})

For disc

a_{2} = \frac{2 g \sin θ}{3} (\frac{K^{2}}{R^{2}} = \frac{1}{2})

a_{1} > a_{2}

, so sphere will reach bottom first.

A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude…

Solution