A massive stone pillar $20 \mathrm{m}$ high and of uniform cross section rests on a rigid base and supports a vertical load of $5.0\times {10}^5 \mathrm{N}$ at its upper end. If the compressive stress in the pillar is not exceed $16\times {10}^5 \mathrm{N}/{\mathrm{m}}^2$, what is the minimum cross-sectional area of the pillar? (Density of the stone $=2.5\times {10}^3 \mathrm{kg}/{\mathrm{m}}^3$ take $\left.g=10 \mathrm{N}/\mathrm{kg}.\right)$

A rubber rope of length $8 \mathrm{m}$ 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 = $5 \times {10}^6 \mathrm{N}{\mathrm{m}}^{-2}$ and density of rubber = $1.5\times {10}^6 \mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}.\mathrm{ }$
(Take $g=10 \mathrm{m}{\mathrm{s}}^{-2})$

A thick rope of density $\rho$ and length $L$ is hung from a rigid support. The increase in length of the rope due to its own weight is $(\mathrm{Y}$ is Young's modulus)