Three bodies, a ring, a soild cylinder and a soild sphere roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are identical. Which of the bodies reaches the ground with maximum velocity ?

Explanation

We have obtained acceleration of an object rolling down an inclined plane
`a = (g sin theta)/(1 + I//mr^(2)) = (g sin theta)/((1 + k^(2)//r^(2)))`
For a ring, `I = mr^(2) ' k^(2) = r^(2)`
`:. A_("ring") = (g sin theta)/(1 + 1) = 0.5 sin theta`
For a solid cylinder, `I = (1)/(2) mr^(2) , k^(2) = (1)/(2)r^(2)`
`:. a_("cyl".) = (g sin theta)/(1 + (1)/(2)) = 0.67 g sin theta`
For a soild sphere, `I = (2)/(5)mr^(2) ' k^(2) = (2)/(5)r^(2)`
`:. a_("sph") = (g sin theta)/(1 + 2//5) = 0.71 g sin theta`
As acceleration of the sphere is maximum therefore, the sphere will reach the ground with maximum velocity.