You hang a floodlamp from the end of a vertical steel wire. The floodlamp stretches the wire 0.18 mm and the stress is proportional to the strain. How much would it have stretched (a) if the wire were twice as long? (b) if the wire had the same length but twice the diameter. (c) for a copper wire of the orIginal length and diameter?
Solution 87P Introduction We have to calculate the stretching of the steel wire if the diameter is doubled or length is doubled. Also we have to calculate the stretching for the copper wire if the length and diameter is same. Step 1 The young’s modulus of the wire is given by So the stretching is given by ………..(1) So from the equation we can see that the stretching is directly proportional to the length of the wire. Hence if the length is doubled then the stretching will also be doubled. Hence the stretching will be Step 2 Now, if d is the diameter of the wire then the area of cross section is So the stretching will be Hence the stretching will be inversely proportional to the square of the diameter. Hence if the diameter is doubled, the stretching will be one fourth of its initial value. Hence the stretching will be