Problem $3$: A vertical $600$ lb force and horizontal force P are applied to a gear$-$and$-$shaft system. Shaft AD has a Modulus of Elasticity value of $29,000$ksi, Modulus of rigidity of $11,460$ksi, and allowable shearing stress of $15$ ksi $.$ Knowing that shaft AD is hollow and that the inner diameter must be $\frac{3}{4}$ of the outer diameter, determine the smallest permissible diameter of shaft AD$.(30$ points$)$

Problem $3$: A vertical $600$ lb force and horizontal force P are applied to a gear$-$and$-$shaft system. Shaft AD has a Modulus of Elasticity value of $29,000$ksi, Modulus of rigidity of $11,460$ksi, and allowable shearing stress of $15$ ksi $.$ Knowing that shaft AD is hollow and that the inner diameter must be $\frac{3}{4}$ of the outer diameter, determine the smallest permissible diameter of shaft AD$.(30$ points$)$