A block of ice and a rubber ball of identical mass are released from rest at the

Question

A block of ice and a rubber ball of identical mass are released from rest at the top of an inclined plane and allowed to descend under the influence of gravity. Assuming that the block of ice slides without friction and that the rubber ball rolls without slipping. Compute the translational speed of the ball when it reaches the bottom of the incline in terms of the translational speed of the block of ice at the bottom of the incline. Treat the ball as a solid sphere of uniform mass density. a) (0.59)Vce c) Vl (0.40 Vc d) ol (0.70)V

Explanation / Answer

here,

for the ice cube

let the height of slope be h

using conservation of energy

0.5 * m * vi^2 = m * g *h

vi = 1.41 * sqrt(g*h) ....(1)

for rubber ball

let the height of slope be h

using conservation of energy

0.5 * m * vb^2 + 0.5 * I * w^2 = m * g *h

0.5 * m * vb^2 + 0.5 *0.4 * m * r^2 * (vb/r)^2 = m * g *h

0.7 * m * vb^2 = m * g *h

vb = 1.1 * sqrt(g*h) ....(2)

from (1) and (2)

vb = 0.7 * vi

so the correct option is d) vb = 0.7 * vi

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