Question

two pieces of the wire of the same material have thier lenth in the ratio 1:2 and diameters in the ratio 2:1 if these are stretched by the same force their alongation will be ​

Answer 1

Answer:

let in two cases, elongation, length, and diameter of wires be (x1, x2), (L1, L2) and (r1, r2) respectively. Force applied be F. Therefore;

[(F/pi* r1^2)/(x1/L1)] = [(F/pi*r2^2)/(x2/L2)]

F & pi will cancel both side. And will solve to

x1/x2 = (L1/L2) * (r2^2/r1^2)

or x1/x2 = (1/2)*(1/4) = 1/8

elongation in wire 2 will be 8 times as compared to wire 1.