Find the total kinetic energy of the system, when the weight is moving at a speed v.?

Question

A circular disk with a mass m and radius R is mounted at its center, about which it can rotate freely. The disk has moment of inertia I = 1/2 mR^2
A light cord wrapped around it supports a weight mg.
Find the total kinetic energy of the system, when the weight is moving at a speed v. Pick best one:

(all are set equal to K)
1. K = 5/4 mv^2
2. = 3/4 mv^2
3. = 1/3 mv^2
4. = 1/2 mv^2
5. = 2/3 mv^2
6. = mv^2
7. = 3/2 mv^2
8. = 4/5 mv^2
9. = 5/2 mv^2

Answer 1

KE = ½ I ω² + ½ m v²

ω = v / R
I = ½ m R²

KE = ½ * (½ m R²) * (v² / R²) + ½ m v²
KE = ¼ m v² + ½ m v²
KE = ¾ m v²

This is choice 2.

Answer 2

K= 1/2 Iw^2 + 1/2 mv^2

w= v/r

K= 1/2 (1/2 mR^2) * (v/r)^2 + 1/2 mv^2

K= 1/4 mv^2 + 1/2 mv^2

K= 3/4 mv^2

So, the answer is #6.