Question

The lengths and radii of 2 wires of same material are 'l' & '2l' and 'r' & 'r|2' respectively ; If both the wires are stretched by the same force , then what will be the ratio of elongation?

Answer 1

Answer: ratio of elongation of wire 1 and 2 Will be 2: 1

Explanation:

Here, Young's modulus is given by

E=Linear stress/linear strain

Which is

E=(F/A)/(dl/l)

=Fl/A.dl

Therefore,

Change in length or elongation is dl which is

dl=Fl/AE

Now it is given as the wires are made of same materials and Same forces are applied then F and E will be constant and thus independent of results.

Hence, the ratio of wires will be

dl1/dl2= (l1/l2)/(A1/A2)

Hence according the given ratio the relationship will be

=l1.R2²/l2R1²

=l.4R²/2l.R²

=2

Hence dl1:dl2= 2: 1