Question

Two wires of the same material have diameters in the ratio 2 : 1 and lengths in the ratio 1 : 2. if they are stretched with same force then ratio of their elongation will be

Answer 1

Stress = Force / Area of cross section.

Area of cross section depends on square of radius, so the ratio of areas is 4:1

Stress is inversely proportional to area so the ratio of stresses will be 1:4

Answer 2

Answer:

1:8

Step-by-step explanation:

Youngs modulus is stress/strain.(longitudinal)

Wires are same it means youngs modulus is same. Stretched by the same force. Thus have only diffences in their areas and lengths.

Wire 1 (elongation)/ wire 2 = F*L1/(A1*Y)/ F*L2/(A2*Y) = L1 A2/ L2 A1. Substitute the ratios you would get the answer.