Question

The length of a metal wire is 10 cm when the tension in it is 20 Newton and 12 centimetre when the tension is 40 Newton. The natural length of the wire is centimetre?

Answer 1

Let the original length of the wire be 'L' now, we have in the first case L1= L + dl1 or [from Hooke's Law; x = T/k] L1= L + (T1/k) .................(1) similarly, for the second case we will have L1= L + dl2 or L2= L + (T2/k) .................(2) we can now use (1) and (2) to solve for original length 'L' so, we get L = (L1T2- L2T1) / (T2- T1) we have L1=10 L2=12 T1=20N T2=40N putting the values we get L=8cm