First slide

Rolling motion

Question

A disc and a sphere of same radius but different masses are rolling down two inclined planes of the same altitude and length.Which one of the two objects gets to the bottom of the plane first?

Moderate

A

Disc
B

Sphere
C

Both reach at the same time
D

Depends on their masses

Solution

Time to roll down the plane is given by $T = \sqrt{\frac{2 L}{a}}$
$a = \frac{g \sin θ}{1 + \frac{K^{2}}{R^{2}}}$
For disc $\frac{K^{2}}{R^{2}} = \frac{1}{2} = 0.5$
For sphere $\frac{K^{2}}{R^{2}} = \frac{2}{5} = 0.4$
a(sphere) > a (disc)
sphere reaches first

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