A wire elongates by $l$ $mm$ when a load $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends, the elongation of the wire will be (in $mm$)
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The ratio of the lengths of two wires $A$ and $B$ of same material is $1 : 2$ and the ratio of their diameter is $2 : 1.$ They are stretched by the same force, then the ratio of increase in length will be
The bulk modulus of rubber is $9.1\times 10^8\,N/m^2$. To ......... $m$ depth a rubber ball be taken in a lake so that its volume is decreased by $0.1\,\%$ .
Two metallic wires $P$ and $Q$ have same volume and are made up of same material. If their area of cross sections are in the ratio $4: 1$ and force $F_1$ is applied to $\mathrm{P}$, an extension of $\Delta l$ is produced. The force which is required to produce same extension in $Q$ is $\mathrm{F}_2$.The value of $\frac{\mathrm{F}_1}{\mathrm{~F}_2}$ is__________.
When a certain weight is suspended from a long uniform wire, its length increases by one $cm$. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one, the increase in length will be ......... $cm$
A steel wire of length ' $L$ ' at $40^{\circ}\,C$ is suspended from the ceiling and then a mass ' $m$ ' is hung from its free end. The wire is cooled down from $40^{\circ}\,C$ to $30^{\circ}\,C$ to regain its original length ' $L$ '. The coefficient of linear thermal expansion of the steel is $10^{-5} { }^{\circ}\,C$, Young's modulus of steel is $10^{11}\, N /$ $m ^2$ and radius of the wire is $1\, mm$. Assume that $L \gg $ diameter of the wire. Then the value of ' $m$ ' in $kg$ is nearly
A substance breaks down by a stress of $10^6 N/m^2$. If the density of the material of the wire is $3×10^3 kg/m^3$, then the length of the wire of the substance which will break under its own weight when suspended vertically, is ......... $m$
A material has Poisson's ratio $0.5$. If a uniform rod of it suffers a longitudinal strain of $3 \times 10^{-3}$, what will be percentage increase in volume is .......... $\%$
When a force is applied on a wire of uniform cross-sectional area $3 \times {10^{ - 6}}\,{m^2}$ and length $4m$, the increase in length is $1\, mm.$ Energy stored in it will be $(Y = 2 \times {10^{11}}\,N/{m^2})$