Solveeit Logo
Login

Question

Physics Question on mechanical properties of solids

A uniform wire (Young?s modulus 2×1011 Nm−22 \times 10^{11}\,Nm^{-2}) is subjected to longitudinal tensile stress of 5×107 Nm−25 \times 10^{7}\,Nm^{-2}. If the overall volume change in the wire is 0.02%0.02\%, the fractional decrease in the radius of the wire is close to:

A

1.0×1041.0 \times 10^{4}

B

1.5×1041.5 \times 10^{4}

C

0.25×1040.25 \times 10^{4}

D

5×1045 \times 10^{4}

Answer

0.25×1040.25 \times 10^{4}

Explanation

Solution

Given, y=2×1011 Nm−2y=2\times10^{11}\,Nm^{-2}
Stress (FA)=5×107 Nm−2\left(\frac{F}{A}\right)=5\times 10^{7}\,Nm^{-2}
ΔV=0.02%=2×10−4 m3\Delta V=0.02\%=2\times 10^{-4}\,m^{3}
Δrr=?\frac{\Delta r}{r}=?
γ=stressstrain⇒strain(Δℓℓ0)=γstress...(i)\gamma=\frac{stress}{strain} \Rightarrow strain \left(\frac{\Delta\ell}{\ell_{0}}\right)=\frac{\gamma}{stress} ...\left(i\right)
ΔV=2πrℓ0Δr−πr2 Δℓ...(ii)\Delta V=2\pi r\ell_{0} \Delta r-\pi r^{2}\,\Delta\ell ...\left(ii\right)
From eqns (i) and (ii) putting the value of
Δℓ,ℓ0\Delta\ell, \ell_{0} and ΔV\Delta V and solving we get
Δrr=0.25×10−4\frac{\Delta r}{r}=0.25\times10^{-4}