Four round objects namely a ring, a disc, a hollow sphere and a solid sphere with same radius R and made of same material start to roll down an inclined plane at the same time. The object that will reach the bottom third is

Explanation

For all the four objects namely the ring, disc, hollow sphere and solid sphere, the radii of gyration K are `R, sqrt((1)/(2))R, sqrt((2)/(3))R, sqrt((2)/(5))R`. With numerical values the radius of gyration K are
IR, 0.707R, 0.816R 0.632R respectively. The expression for time taken for rolling has the radius of gyration K in the numerator as per equation `Vsqrt((2gh)/((1+(K^(2))/(R^(2)))))`
`t= sqrt((2h(1+(K^(2))/(R^(2))))/(g sin^(2) theta))`
The one with least value of radius of gyration K will take the shortest time to reach the bottom of the inclined plane. The order of objects reaching the bottom is first, solid sphere, second, dise: third, hollow sphere and last, rin