A ring, a disc and a sphere all of the same radius andmass roll down an inclined plane from the same height h. Which of the three reaches bottom (i) earliest (ii) latest ?

A ring, a disc and a sphere all of the same radius andmass roll down a

1.	A ring, a disc and a sphere all of the same radius andmass roll down an inclined plane from the same height h. Which of the three reaches bottom (i) earliest (ii) latest ?
Answer» Solution :The ACCELERATION attained by the centre of mass of a rolling body down an inclined plane is `a =(g sin THETA)/(1 + I/(MR^(2))` For a ring, `I = MR^(2), a_(r) (g sin theta)/2` For a disc `I = 1/2 MR^(2), a_(d) = (g sin theta)/(1+1/2) = (2g sin theta)/3` For sphere, `I = 2/5 MR^(2), a_(s) = (g sin theta)/(1 +2/5) = (5g)/7 sin theta` Thus, `a_(r) lt a_(d) lt a_(s)`.They all start from rest. So the sphere will reach bottom FIRST and the ring last.