A disc and a sphere of same radius but different masses roll off on two inclined planes of the same attitude and length. Which one of the two objects gets of 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

Acceleration on slope `a=(gsintheta)/(1+(k^(2))/(R^(2)))`
`therefore aprop(1)/(1+(k^(2))/(R^(2)))`
`therefore` Acceleration of sphere `a_(s)prop(1)/(1+(2R^(2))/(5R^(2)))=(5)/(7)`
`therefore` Acceleration of disc `a_(d)prop(1)/(1+(R^(2))/(2R^(2)))=(2)/(3)`
`therefore (a_(s))/(a_(d))=(5)/(7)xx(3)/(2)=(15)/(14)gt1`
`therefore a_(s)gta_(d)`
`therefore` Acceleration of sphere is more then acceleration of disc and hence sphere reach at first on the bottom.