If the moment of inertia of wheel is found to be 1/2mr2 then which of the following will represent the velocity when it rolls down from. A height of "H" TO the ground?

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Answer 1 · 2018-07-12T21:01:16

#v=2\sqrt{{gH}/3}#

Assuming there is no loss of energy then the total energy of the wheel will be conserved.

Let #v# be the velocity of center of mass of wheel when it reaches the ground then by the energy conservation ,

#\text{potential energy of wheel at a height } H=\text{kinetic energy of wheel on ground}#

#mgH=1/2mv^2+1/2I\omega^2#

#mgH=1/2mv^2+1/2(1/2mr^2)(v/r)^2\ \quad (\because\omega=v/r)#

#gH=1/2v^2+1/4v^2#

#gH=3/4v^2#

#v^2=4/3gH#

#v=2\sqrt{{gH}/3}#