Q. When a certain weight is suspended from a long uniform wire, its length increases by 1 cm. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one, the increase in length will be
A) 0.5 cm
B) 2 cm
C) 4 cm
D) 8 cm
Explanation
(c) $Y = \frac{Fl}{\alpha\mathrm{\Delta}L}\ or\ \mathrm{\Delta}L\ \propto \frac{1}{\alpha};\ \mathrm{\Delta}L\ \propto \frac{1}{D^{2}}\ $
$\frac{\mathrm{\Delta}L_{2}}{\mathrm{\Delta}L_{2}} = \frac{D_{1}^{2}}{D_{2}^{2}} = 4\ or\ \mathrm{\Delta}L_{2} = 4\mathrm{\Delta}L_{1} = 4cm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.