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
$2\,l$
$l$
$4 \ l$
$l / 2$
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 copper wire of length $2.2 \;m$ and a steel wire of length $1.6\; m ,$ both of diameter $3.0 \;mm ,$ are connected end to end. When stretched by a load, the net elongation is found to be $0.70 \;mm$. Obtain the load applied in $N$.
There are two wire of same material and same length while the diameter of second wire is two times the diameter of first wire, then the ratio of extension produced in the wires by applying same load will be
A rod $BC$ of negligible mass fixed at end $B$ and connected to a spring at its natural length having spring constant $K = 10^4\ N/m$ at end $C$, as shown in figure. For the rod $BC$ length $L = 4\ m$, area of cross-section $A = 4 × 10^{-4}\ m^2$, Young's modulus $Y = 10^{11} \ N/m^2$ and coefficient of linear expansion $\alpha = 2.2 × 10^{-4} K^{-1}.$ If the rod $BC$ is cooled from temperature $100^oC$ to $0^oC,$ then find the decrease in length of rod in centimeter.(closest to the integer)
A steel wire of length $4.7\; m$ and cross-sectional area $3.0 \times 10^{-5}\; m ^{2}$ stretches by the same amount as a copper wire of length $3.5\; m$ and cross-sectional area of $4.0 \times 10^{-5} \;m ^{2}$ under a given load. What is the ratio of the Young's modulus of steel to that of copper?