Question

Overall changes in volume and radii of a uniform cylindrical steel wire 0.2% and 0.002% respectively when subjected to some suitable force. Longitudinal tensile stress acting on the wire is?

Answer 1

we know, volume = cross sectional area × length
e.g., V = A × l = πr²l

or, logV = log(πr² × l)

or, logV = logπ + 2logr + logl

differentiate both sides,

± dV/V =± 2dr/r ± dl/l

so, for getting maximum error , dl/l = 2dr/r + dV/V
hence, % change in l = 2 × % change in r + % change in V
=2 × 0.002 % + 0.2 % = 0.204%

so, dl/l = strain = 0.204/100

now, stress = Y × strain

= 2 × 10¹¹ × 0.204/100

= 0.408 × 10^9 N/m² or 4.08 × 10^8 N/m²

hence, tensile stress = 4.08 × 10^8 N/m².

Answer 2

Explanation:

here is the answer for you dear