Question

6.A solid sphere, a solid cylinder, and a hoop all have the same mass and radius. Each are sent down identical inclined planes starting from rest. Their kinetic energies at the bottom of the incline are Ksphere, Kcylinder, and Khoop. Which of the following is true?

a.Ksphere > Kcylinder

b.Khoop > Ksphere

c.Khoop > Kcylinder

d.Kcylinder > Khoop

e.No answer above is correct.

The answer is e, but could someone please explain why

Answer 1

conserving energy both at top and bottom

all 3 have same potential energy at top (as they have same mass)

thus when this potential enery converts to kinetic energy at bottom ..all three must have same kinetic energy(by conservation of energy)

so we have kE of sphere =KE of cylinder= KE of hoop

thus ans is (e)

Answer 2

energy conservation . . .

potential energy (mgh) will convert into kinetic energy (mv^2/2) . but as all have the same maas and radius . so they have same potential energy . thus their kinetic energy will also be same .

Answer 3

Loss in PE = Gain in KE

Since they start from rest:

K = Loss in PE

Now, here the objects are rolled down identical planes from the same height, so loss in PE for each of them is the same. ( PE= mgh)

Thus, Ksphere= Kcylinder= Khoop

e.No answer above is correct.