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When a uniform wire of radius $r$ is stretched by a $2kg$ weight, the increase in its length is $2.00\, mm$. If the radius of the wire is $r/2$ and other conditions remain the same, the increase in its length is .......... $mm$
The extension of a wire by the application of load is $3$ $mm.$ The extension in a wire of the same material and length but half the radius by the same load is..... $mm$
One end of a uniform wire of length $L$ and of weight $W$ is attached rigidly to a point in the roof and a weight ${W_1}$ is suspended from its lower end. If $S$ is the area of cross-section of the wire, the stress in the wire at a height $3L/4$ from its lower end is
A wooden wheel of radius $R$ is made of two semicircular part (see figure). The two parts are held together by a ring made of a metal strip of cross section area $S$ and length $L$. $L$ is slighly less than $2\pi R$. To fit the ring on the wheel, it is heated so that its temperature rises by $\Delta T$ and it just steps over the wheel.As it cools down to surronding temperature, it presses the semicircular parts together. If the coefficint of linear expansion of the metal is $\alpha$, and its young's modulus is $Y$, the force that one part of wheel applies on the other part is
What must be the lengths of steel and copper rods at $0^o C$ for the difference in their lengths to be $10\,cm$ at any common temperature? $(\alpha_{steel}=1.2 \times {10^{-5}} \;^o C^{-1})$ and $(\alpha_{copper} = 1.8 \times 10^{-5} \;^o C^{-1})$
Given : $\sigma$ is the compressibility of water, $\rho$ is the density of water and $K$ is the bulk modulus of water. What is the energy density of water at the bottom of a lake $‘h’$ metre deep ?
Two wires of same diameter of the same material having the length $l$ and $2l.$ If the force $ F$ is applied on each, the ratio of the work done in the two wires will be
The adjacent graph shows the extension $(\Delta l)$ of a wire of length $1\, m$ suspended from the top of a roof at one end and with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-6}\, m^2$, calculate the Young’s modulus of the material of the wire.
The pressure applied from all directions on a cube is $P$. How much its temperature should be raised to maintain the original volume $?$ The volume elasticity of the cube is $\beta $ and the coefficient of volume expansion is $\alpha $