A box and a solid sphere of equal mass are moving with the same velocity across a horizontal floor. The sphere rolls without slipping and the box without friction. They ecounter an upward slope in the floor and each move up the slope some distance before momentarily stopping and then moving downn again. The maximum vertical heights reached by the box and the sphere are `H_(B)` and `H_(s)` respectively. What is the ratio `(5H_(s))/(H_(B))` ?

Answer

7

Explanation

`mgH_(B)=1/2 mv^(2)`
`mgH_(s)=1/2mv^(2)+1/2Iomega^(2)=1/2mv^(2)+1/2xx1/2mr^(2)omega^(2)=1/2xx7/5mv^(2)`
`(H_(s))/(H_(B))=7/5implies(5H_(s))/(H_(B))=7`