1.
Moment of inertia of marble
I = (2/5) mr^2 = 0.4 mr^2
Rotational KE
KEr = 0.5 Iw^2 = 0.5 ( 0.4 mr^2) ( v/r) ^2
KEr = 0.2 mv^2 (I)
Total kinetic energy
KET = 0.5 mv^2 + 0.5 I w^2 = 0.5 mv^2 + 0.5 (0.4 mv^2)
KET = 0.7 mv^2 (ii)
Considering equ (I) and (ii)
KEr/ KET = 0.2/0.7
KEr = (2/7) KET
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Plz post other problems seperately,
Do comment in case any doubt, will reply for sure, Goodluck
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