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A string is wrapped several times on a c...

A string is wrapped several times on a cylinder of mass `M` and radius `R`. the cylinder is pivoted about its adxis of block symmetry. A block of mass `m` tied to the string rest on a support positioned so that the string has no slack. The block is carefully lifted vertically a distance `h`, and the support is removed as shown figure.
a. just before the string becomes taut evalute the angular velocity `omega_(0)` of the cylinder ,the speed `v_(0)` of the falling body, `m` and the kinetic energy `K_(0)` of the system.
b. Evaluate the corresponding quanitities `omega_(1), v_(1)` and `K_(1)` for the instant just after the string becomes taut.
c. Why is `K_(1)` less than `K_(0)`? Where does the energy go?
d. If `M=m`, what fraction of the kinetic energy is lost when the string becomes taut?

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