A ring of mass 0.3 kg and radius 0.1 m and a solid cylinder of mass 0.4 kg and of the same radius are
given the same kinetic energy and released simultaneously on a flat horizontal surface such that they
being to roll as soon as released
(c) Both will reach the wall simultaneously.
KE of a rolling body = KE translational + KE rotational
= (1/2)MVcm2 + (1/2)Iw2 =(1/2)[(MVcm2 + I(Vcm/R)2]
= (1/2)[(MVcm2 + I(Vcm/R)2] = (Vcm2 /2)(M + I/R2) = (MVcm2 /2)(1 + c)
... since I = cMR2 , for example, for ring I = MR2, hence c = 1.
Now since both have the same KE,
Vcm = (2KE/((1 + c)M))1/2
(Vcm)ring/(Vcm)cylinder = (1/((1+c)M)ring1/2/(1/((1+c)M)cylinder1/2
(Vcm)ring/(Vcm)cylinder = = ((1.5x0.4)/(0.3x2)1/2 = 1
Both are moving at the same speed, and will reach at the same time.