Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of the same material and the radius of wire B is 4 times that of the radius of wire A. The lengths of the wires A and B are in the ratio of a:b.…

Question

Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of the same material and the radius of wire B is 4 times that of the radius of wire A. The lengths of the wires A and B are in the ratio of a:b. Then a/b can be expressed as 1/x, where x is .

Accepted Answer

32. Given: the same material and the same force F=2 N, with r_B=4r_A. Δ l=(FL)/(π r²Y), so L=(π r²Y Δ l)/F and L∝ r²Δ l. (L_A)/(L_B)=((r_A)/(r_B))²×(Δ l_A)/(Δ l_B)=1/(16)×2/4. (L_A)/(L_B)=1/(32). Hence x=32.

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