A very light 1.00-m wire consists of two segments of equal length,one of steel (Young's modulus is 2.00 × 10¹¹ N/m²)and one of brass (Young's modulus is 9.0 × 10¹⁰ N/m²).The steel segment is 1.50 mm in diameter,and the brass segment has twice this diameter.When a weight w is hung from the ceiling by this wire,the steel segment stretches by 1.10 mm.By what distance does the brass segment stretch? A)0.50 mm B)0.61 mm C)1.2 mm D)2.4 mm E)9.8 mm

Question

Quizplus · Accepted Answer

First, we need to find the force applied to the wire by the weight w. We can use the equation F = mg, where m is the mass of the weight and g is the acceleration due to gravity. 
Next, we need to find the cross-sectional areas of each segment of the wire. Since the brass segment has twice the diameter of the steel segment, it has four times the cross-sectional area. 
Using the equation for Young's modulus, stress = (force/area) = (Y*strain), we can find the strain in each segment of the wire. Since the two segments are of equal length and the steel segment stretches by 1.10 mm, the total elongation of the wire is 2.20 mm. We can use this information to find the strain in the steel segment, and then use the ratio of the cross-sectional areas to find the strain in the brass segment. 
Finally, we can use the equation for strain to find the elongation of the brass segment.

After doing all the calculations, we get that the brass segment stretches by 0.61 mm. Therefore, the answer is B.

A Very Light 1