Question

Two shafts of solid circular cross-section are identical except for their diameter ${}^{\prime }{d}_1^{\prime }and{}^{\prime }{d}_2^{\prime }$. They are subjected to the same torque T. The ratio of the strain energies stored $U_1/U_2$ will be

• A. ${\left(\frac{d_1}{d_2}\right)}^4$
• B. ${\left(\frac{d_1}{d_2}\right)}^2$
• C. ${\left(\frac{d_2}{d_1}\right)}^2$
• D. ${\left(\frac{d_2}{d_1}\right)}^4$

Answer 1

The correct option is D ${\left(\frac{d_2}{d_1}\right)}^4$

$StrainenergyU=\frac{1}{2}T\theta$

$and\theta =\frac{TL}{GJ}$

$\therefore U=\frac{T^{2}L}{2GJ}$

$J=\frac{\pi d^4}{32}$

$\therefore \frac{U_1}{U_2}$=${\left(\frac{d_2}{d_1}\right)}^4$