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The area of cross-section of a railway track is $0.01\, {m}^{2}$. The temperature variation is $10^{\circ} {C}$. Coefficient of linear expansion of material of track is $10^{-5} /{ }^{\circ} {C}$. The energy stored per meter in the track is ...... ${J} / {m} .$
(Young's modulus of material of track is $10^{11} \,{Nm}^{-2}$ ))
A rigid bar of mass $15\,kg$ is supported symmetrically by three wire each of $2 \,m$ long. These at each end are of copper and middle one is of steel. Young's modulus of elasticity for copper and steel are $110 \times 10^9 \,N / m ^2$ and $190 \times 10^9 \,N / m ^2$ respectively. If each wire is to have same tension, ratio of their diameters will be ............
A wire of cross sectional area $A$, modulus of elasticity $2 \times 10^{11} \mathrm{Nm}^{-2}$ and length $2 \mathrm{~m}$ is stretched between two vertical rigid supports. When a mass of $2 \mathrm{~kg}$ is suspended at the middle it sags lower from its original position making angle $\theta=\frac{1}{100}$ radian on the points of support. The value of $A$ is. . . . . . $\times 10^{-4} \mathrm{~m}^2$ (consider $\mathrm{x}<\mathrm{L}$ ).
Two wires of the same material (Young's modulus $Y$ ) and same length $L$ but radii $R$ and $2R$ respectively are joined end to end and a weight $W$ is suspended from the combination as shown in the figure. The elastic potential energy in the system is
An aluminium rod with Young's modulus $Y =7.0$ $\times 10^{10} N / m ^2$ undergoes elastic strain of $0.04 \%$. The energy per unit volume stored in the rod in SI unit is:
When a block of mass $M$ is suspended by a long wire of length $L$, the length of the wire become $(L+l) .$ The elastic potential energy stoped in the extended wire is :
A metal wire of length $L_1$ and area of cross section $A$ is attached to a rigid support. Another metal wire of length $L_2$ and of the same cross sectional area is attached to the free end of the first wire. A body of mass $M$ is then suspended from the free end of the second wire. If $Y_1$ and $Y_2$ are the Youngs moduli of the wires respectively, the effective force constant of the system of two wires is :