(Solved): A slender 7.5kg rod can rotate in a vertical plane about a pivot at A. A spring of constant k= ...

A slender $$7.5?\mathrm{kg}$$ rod can rotate in a vertical plane about a pivot at A. A spring of constant $$\mathrm{k}=$$ $$241\mathrm{N}/\mathrm{m}$$ and of unstretched length $$250\mathrm{mm}$$ is attached to the rod as shown. Knowing that the rod is released from rest in position (1) $$\left(?=0^{?}\right)$$, it has rotated through $$90^{?}$$ to reach position (2) $$\left(?=90^{?}\right)$$. For $$L=780\mathrm{mm}$$ kinetic energy at position (1) (Joules) moment of inertia about the hinge $$\left(\mathrm{kg}?{\mathrm{m}}^2\right)$$ a. $$1.83$$ b. $$1.52$$ c. $$1.22$$ d. $$0.91$$ e. $$0.61$$ work due spring (N.m) work due to weight (N.m) ?. $$?40.13$$ b. $$?34.4$$ c. $$?22.93$$ 1. $$?28.67$$ ?. $$?45.86$$ angular velocity in position (2) $$(\mathrm{rad}/\mathrm{s})$$ a. $$18.73$$ b. $$14.04$$ c. $$11.7$$ d. $$16.39$$ e. $$4.68$$