Two wires A and B are made of same material. The wire A has a length l and diameter r while the wire B has a length 2l and diameter r/2.
Two wires A and B are made of same material. The wire A has a length l and diameter r while the wire B has a length 2l and diameter r/2.If the two wires are stretched by the same force, the elongation in A divided by the elongation in B is
(a) 1/8
(b) 1/4
(c) 4
(d) 8.
1 Answers
The correct answer is (a) 1/8
Explanation:
For wires of the same material, the elongation is directly proportional to the length and inversely proportional to the cross-sectional area.
Δl/l = F/AY
→Δl =Fl/AY {Here F and Y are constant}
The length of A is half of B, for it, elongation of A will be ½ of B and the area of A is four times of B (Since the area is proportional to the square of the radius), for it, the elongation of A will be ¼th of B. For the combined effect of both length and the area, the elongation of A will be ½*¼ =1/8 of B.