A disc 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

A. sphere
B. both reach at the same time
C. depends on their masses
D. disc

Answer

A

Explanation

In case of rolling down on the plane, time taken by an object to reach to the bottom of the plane,
t = `(1)/(sin theta) sqrt((2h)/(g) (1 + (k^(2))/(R^(2))) ) `
[ where, h = the vertical height from which the object starts to roll down, `theta` = angle of inclination of the plane]
In case of the disc, `(k^(2))/(R^(2)) = (1)/(2) = 0.5 `
In case of the sphere, `(k^(2))/(R^(2)) = (2)/(5) = 0.4 `
`therefore` the time taken by the sphere is less than the disc to reach to the bottom of the plane.
Hence, the sphere gets to the bottom of the plane first.