In an experiment, brass and steel wires of length $1\,m$ each with areas of cross section $1\,mm^2$ are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress requires to produced a new elongation of $0.2\,mm$ is [Given, the Young’s Modulus for steel and brass are respectively $120\times 10^9\,N/m^2$ and $60\times 10^9\,N/m^2$ ]

A mild steel wire of length $1.0 \;m$ and cross-sectional area $0.50 \times 10^{-2} \;cm ^{2}$ is stretched, well within its elastic limit, horizontally between two pillars. A mass of $100 \;g$ is suspended from the mid-point of the wire. Calculate the depression at the midpoint.

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 rubber cord catapult has cross-sectional area $25\,m{m^2}$ and initial length of rubber cord is $10\,cm.$ It is stretched to $5\,cm.$ and then released to project a missile of mass $5gm.$ Taking ${Y_{rubber}} = 5 \times {10^8}N/{m^2}$ velocity of projected missile is ……… $ms^{-1}$

A wire of length $L$ and radius $r$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$, its length increases by $l$. Another wire of same material of length $2 L$ and radius $2 r$ is pulled by a force $2 f$. Then the increase in its length will be