A copper wire $(Y = 1 \times 10^{11}\, N/m^2)$ of length $6\, m$ and a steel wire $(Y = 2 \times 10^{11}\, N/m^2)$ of length $4\, m$ each of cross section $10^{-5}\, m^2$ are fastened end to end and stretched by a tension of $100\, N$. The elongation produced in the copper wire is ......... $mm$
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Consider two wires of same material having their ratio of radii to be $2: 1$. If these two wires are stretched by equal force, then the ratio of stress produced in them is
A compressive force, $F$ is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by $\Delta T$. The net change in its length is zero. Let $l$ be the length of the rod, $A$ its area of cross- section, $Y$ its Young's modulus, and $\alpha $ its coefficient of linear expansion. Then, $F$ is equal to
A uniform copper rod of length $50 \,cm$ and diameter $3.0 \,mm$ is kept on a frictionless horizontal surface at $20^{\circ} C$. The coefficient of linear expansion of copper is $2.0 \times 10^{-5} \,K ^{-1}$ and Young's modulus is $1.2 \times 10^{11} \,N / m ^2$. The copper rod is heated to $100^{\circ} C$, then the tension developed in the copper rod is .......... $\times 10^3 \,N$
Two wires of equal lengths are made of the same material. Wire $A$ has a diameter that is twice as that of wire $B$. If identical weights are suspended from the ends of these wires, the increase in length is
$Assertion :$ Hollow shaft is found to be stronger than a solid shaft made of same equal material.
$Reason :$ Torque required to produce a given twist in hollow cylinder is greater than that required to twist a solid cylinder of same length and material.
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 :