Given & Known Data:m = 45 kg is the mass of the traffic light.r = 0.50 cm = 0.0050 m is the radius of the steel cable. 0= 15° is the angle made by the cable with the horizontal.E = 20 × 1010 N m2 is Young's modulus of steel.The traffic light is in static equilibrium condition. So in the vertical direction, we will be using the translational equilibrium condition. sum Fy =0 T x sin + T x sinθ - W = 0 T x sinθ + T x sinθ = W T x sinθ + T x sinθ = mg T - \\[\\frac {(mg)} {(2\\sin\ heta)}\\]= 45 kg x 9.81 m s2 2 x sin15 = approx 852.82 N Therefore, the tension in the cable is 852.82 N.Now, we'll calculate the fractional increase in the length of the cable :Delta x L = \\[\\frac {(TL)} {(AE)}\\](Delta x L)/L = \\[\\frac {T} {(AE)}\\]= T ( pi r2 )E = 5.4 x 105Hence, Due to the weight of traffic lights, the fractional increase in length of the cable is 5.4 x 105.