To double the length of a iron wire having $0.5\,c{m^2}$ area of cross-section, the required force will be $(Y = {10^{12}}\,dyne/c{m^2})$
$1.0 \times {10^{ - 7}}N$
$1.0 \times {10^7}N$
$0.5 \times {10^{ - 7}}N$
$0.5 \times {10^{12}}$dyne
Young’s modulus of perfectly rigid body material is
A beam of metal supported at the two ends is loaded at the centre. The depression at the centre is proportional to
A metal rod of cross-sectional area $10^{-4} \,m ^{2}$ is hanging in a chamber kept at $20^{\circ} C$ with a weight attached to its free end. The coefficient of thermal expansion of the rod is $2.5 \times 10^{-6} \,K ^{-1}$ and its Young's modulus is $4 \times 10^{12} \,N / m ^{2}$. When the temperature of the chamber is lowered to $T$, then a weight of $5000 \,N$ needs to be attached to the rod, so that its length is unchanged. Then, $T$ is ............ $^{\circ} C$
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.
Two wires $A$ and $B$ are of same materials. Their lengths are in the ratio $1 : 2$ and diameters are in the ratio $2 : 1$ when stretched by force ${F_A}$ and ${F_B}$ respectively they get equal increase in their lengths. Then the ratio ${F_A}/{F_B}$ should be