$A$ stone of mass $20 \, g$ is projected from a rubber catapult of length $0.1 \, m$ and area of cross-section $10^{-6} \, m^2$,stretched by an amount $0.04 \, m$. The velocity of the projected stone is $.... \, m/s$. (Young's modulus of rubber $= 0.5 \times 10^9 \, N/m^2$)

$A$ boy's catapult is made of a 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 $20\, m/s$. Neglect the change in the area of cross-section of the cord while stretched. The Young's modulus of rubber is closest to:

$A$ rubber cord catapult has a cross-sectional area of $25\,mm^2$ and an initial length of $10\,cm$. It is stretched by $5\,cm$ and then released to project a missile of mass $5\,g$. Taking $Y_{rubber} = 5 \times 10^8\,N/m^2$,the velocity of the projected missile is ......... $m/s$.

Two wires having the same length and material are stretched by the same force. Their diameters are in the ratio $1:3$. The ratio of strain energy per unit volume for these two wires (smaller to larger diameter),when stretched,is (in $:1$)

The work done in increasing the length of a $1 \, m$ long wire of cross-sectional area $1 \, mm^2$ by $1 \, mm$ is (Given $Y = 2 \times 10^{11} \, N/m^2$): (in $, J$)

If one end of a wire is fixed with a rigid support and the other end is stretched by a force of $10 \, N$,then the increase in length is $0.5 \, mm$. The ratio of the energy stored in the wire to the work done in displacing it through $1.5 \, mm$ by the weight is