A solid sphwere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights `h_(sph)` and `h_(cyl)` on the incline. The ratio `(h_(sph)/(h(cyl)))` is given by :

Options

A. 1
B. `2/sqrt(5)`
C. `14/15`
D. `4/5`

Answer

C

Explanation

`KE_(sph) = 1/2 mv^(2) + 1/2Iomega^(2) = 1/2mv^(2) +1/2(2/5 mR^(2))(v^(2)/R^(2))`
`=1/2 mv^(2) (1+2/5) = 7/5(1/2 mv^(2))`
Maximum `ht = h(sph), mgh_(sph) =7/5 (1/2 mv^(2)) rArr h_(sph) = 7/5 (v^(2)/(2g))`
Similarly,
`h_(cyl) =3/2(v^(2)/(2g)) rArr h_(sph)/h_(cyl) =(7//5)/(3//2) = 14/15`