As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of $45^{\circ}$ with the load axis. The length of wire is $62.8\,cm$ and its diameter is $4\,mm$. The Young's modulus is found to be $x \times$ $10^4\,Nm ^{-2}$. The value of $x$ is
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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
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 $
A steel rod has a radius $10 \,mm$ and a length of $1.0 \,m$. A force stretches it along its length and produces a strain of $0.32 \%$. Young's modulus of the steel is $2.0 \times 10^{11} \,Nm ^{-2}$. What is the magnitude of the force stretching the rod is ........ $kN$
Wires $A$ and $B$ are connected with blocks $P$ and $Q$ as shown. The ratio of lengths, radii and Young's modulus of wires $A$ and $B$ are $r, 2r$ and $3r$ respectively ($r$ is a constant). Find the mass of block $P$ if ratio of increase in their corresponding lengths is $1/6r^2$. The mass of block $Q$ is $3M$.
The breaking stress of aluminium is $7.5 \times 10^7 \,Nm ^{-2}$. The greatest length of aluminium wire that can hang vertically without breaking is ......... $\times 10^3 \,m$ (Density of aluminium is $2.7 \times 10^3 \,kg m ^{-3}$ )