P$-4($a$)$ If the allowable tensile stress for wires AB and AC is ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=200$MPa, determine the required diameter of each wire if the applied load is $P=6kN.$

$($b$)$ If the allowable tensile stress for wires AB and AC is ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=180$MPa, and wire $AB$ has a diameter of $5$ mm and $AC$ has a diameter of $6$ mm $,$ determine the greatest force $P$ that can be applied to the chain.