A string of a material of length $1 \mathrm{m},$ cross-sectional area $0.2 {\mathrm{cm}}^2$ requires $2000 \mathrm{N}$ to extend it by $1 \mathrm{mm}$. The same material is used to manufacture the legs of a robot of $50 \mathrm{cm}$ length and of cross-sectional area $0.5 {\mathrm{cm}}^2$ each. The mass of the robot is $50 \mathrm{kg}$. When it jumps from a building of height $h$, it experiences a strain $0.05.$ The maximum height through which the robot can jump without breaking its legs is $\left(\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A uniform cylindrical rod of length $L$ , area of cross-section $A$ and Young's modulus $Y$ is acted upon by the forces as shown in the figure. The elongation of the rod is

A block of wood floats in water with $(4/5{)}^{\mathrm{th}}$ of its volume submerged. If the same block just floats in a liquid, then find the density of this liquid. (Given density of water $=1000 \mathrm{kg} {\mathrm{m}}^{-3}$ )

A cylindrical tank has a hole of $1{ \mathrm{cm}}^2$ in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of $70{ \mathrm{cm}}^3 {\mathrm{s}}^{-1}$, then the maximum height up to which water can rise in the tank is_________