A boy’s catapult is made of rubber cord which is $42\, cm$ long, with $6\, mm$ diameter of cross -section and of negligible mass. The boy keeps a stone weighing $0.02\, kg$ on it and stretches the cord by $20\, cm$ by applying a constant force. When released, the stone flies off with a velocity of $20\, ms^{-1}$. Neglect the change in the area of cross section of the cord while stretched. The Young’s modulus of rubber is closest to

A uniformly tapering conical wire is made from a material of Young's modulus $Y$  and has a normal, unextended length $L.$ The radii, at the upper and lower ends of this conical wire, have values $R$ and $3R,$  respectively. The upper end of the wire is fixed to a rigid support and a mass $M$ is suspended from its lower end. The equilibrium extended length, of this wire, would equal 

A compressive force, $F$ is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by $\Delta T$. The net change in its length is zero. Let $l$ be the length of the rod, $A$ its area of cross- section, $Y$ its Young's modulus, and $\alpha $ its coefficient of linear expansion. Then, $F$ is equal to

The area of cross section of a steel wire $(Y = 2.0 \times {10^{11}}N/{m^2})$ is $0.1\;c{m^2}$. The force required to double its length will be

The length of a wire is $1.0\, m$ and the area of cross-section is $1.0 \times {10^{ - 2}}\,c{m^2}$. If the work done for increase in length by $0.2\, cm$ is $0.4\, joule$, then Young's modulus of the material of the wire is

The Young's modulus of a wire is $y$. If the energy per unit volume is $E$, then the strain will be