Q. A rubber rope of length 8 m is hung from the ceiling of a room. What is the increase in length of the rope due to its own weight ? (Given Young’s modulus of elasticity of rubber = $5\ \times 10^{6}\ Nm^{- 2}$ and density of rubber = $1.5 \times 10^{6}\ kgm^{- 3}.\ $ Take g = 10 $ms^{- 2})$
A) 1.5 mm
B) 6 mm
C) 24 mm
D) 96 mm
Explanation
(d) $Y = \frac{Mg}{A}\ \times \ \frac{L/2}{\mathrm{\Delta}L}$
(Length is taken as $\frac{L}{2}$ because weight acts as CG )
Now, $M = AL\rho$
(For the purpose of calculation of mass, the whole of geometrical length L is to be considered.)
$\therefore\ \ Y = \frac{ALpgL}{2A\mathrm{\Delta}L}\ $
Or $\mathrm{\Delta}L = \frac{pgL^{2}}{2Y} = \ \frac{1.5 \times 10^{3} \times 10 \times 8 \times 8}{2\ \times 5\ \times 10^{6}}$
= 9.6 $\times 10^{- 2}m = 9.6\ \times 10^{- 2} \times 10^{3}\ mm$
= 96 mms
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.