The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If ${Y_A}$ and ${Y_B}$ are the Young ‘s modulii of the materials, then
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A bob of mass $10\, kg$ is attached to wire $0.3\, m$ long. Its breaking stress is $4.8 \times 10^7 N/m^2$. The area of cross section of the wire is $10^{-6} m^2$. The maximum angular velocity with which it can be rotated in a horizontal circle ....... $rad/sec$
The strain-stress curves of three wires of different materials are shown in the figure. $P, Q$ and $R$ are the elastic limits of the wires. The figure shows that
If $\rho $ is the density of the material of a wire and $\sigma $ is breaking stress, the greatest length of the wire that can hang freely without breaking is
A solid sphere of radius $r$ made of a soft material of bulk modulus $K$ is surrounded by a liquid in a cylindrical container. A massless piston of area $a$ floats on the surface of the liquid, covering entire crosssection of cylindrical container. When a mass $m$ is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, $\left( {\frac{{dr}}{r}} \right)$ is
The length of a rod is $20\, cm$ and area of cross-section $2\,c{m^2}$. The Young's modulus of the material of wire is $1.4 \times {10^{11}}\,N/{m^2}$. If the rod is compressed by $5\, kg-wt$ along its length, then increase in the energy of the rod in joules will be