A wire of length $L$ and radius $r$ is clamped at one end. If its other end is pulled by a force $F$, its length increases by $l$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become.

Under the same load, wire $A$ having length $5.0\,m$ and cross section $2.5 \times 10^{-5}\,m ^2$ stretches uniformly by the same amount as another wire $B$ of length $6.0\,m$ and a cross section of $3.0 \times 10^{-5}\,m ^2$ stretches. The ratio of the Young's modulus of wire $A$ to that of wire $B$ will be

A steel rod of length $1\,m$ and area of cross section $1\,cm^2$ is heated from $0\,^oC$ to $200\,^oC$ without being allowed to extend or bend. Find the tension produced in the rod $(Y = 2.0 \times 10^{11}\,Nm^{-2}$,  $\alpha = 10^{-5} C^{-1})$ 

The modulus of elasticity is dimensionally equivalent to

The diameter of a brass rod is 4 mm and Young's modulus of brass is $9 \times {10^{10}}\,N/{m^2}$. The force required to stretch by $0.1\%$ of its length is

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 ......... $ms^{-1}$