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The Young's modulus of a rubber string $8\, cm$ long and density $1.5\,kg/{m^3}$ is $5 \times {10^8}\,N/{m^2}$, is suspended on the ceiling in a room. The increase in length due to its own weight will be
A wire extends by $1 mm$ when a force is applied. Double the force is applied to another wire of same material and length but half the radius of cross-section. The elongation of the wire in mm will be ........
A rubber cord catapult has cross-sectional area $25\,m{m^2}$ and initial length of rubber cord is $10\,cm.$ It is stretched to $5\,cm.$ and then released to project a missile of mass $5gm.$ Taking ${Y_{rubber}} = 5 \times {10^8}N/{m^2}$ velocity of projected missile is ......... $ms^{-1}$
A steel wire of length $3.2 m \left( Y _{ S }=2.0 \times 10^{11}\,Nm ^{-2}\right)$ and a copper wire of length $4.4\,M$ $\left( Y _{ C }=1.1 \times 10^{11}\,Nm ^{-2}\right)$, both of radius $1.4\,mm$ are connected end to end. When stretched by a load, the net elongation is found to be $1.4\,mm$. The load applied, in Newton, will be. (Given $\pi=\frac{22}{7}$)
A bar of cross-sectional area $A$ is subjected two equal and opposite tensile forces at its ends as shown in figure. Consider a plane $BB'$ making an angle $\theta $ with the length The ratio of tensile stress to the shearing stress on the plane $BB'$ is
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
If the temperature of a wire of length $2 \,m$ and area of cross-section $1 \,cm ^2$ is increased from $0^{\circ} C$ to $80^{\circ} C$ and is not allowed to increase in length, then force required for it is ............$N$ $\left\{Y=10^{10} \,N / m ^2, \alpha=10^{\left.-6 /{ }^{\circ} C \right\}}\right.$