A substance breaks down by a stress of $10^6 N/m^2$. If the density of the material of the wire is $3×10^3 kg/m^3$, then the length of the wire of the substance which will break under its own weight when suspended vertically, is ......... $m$
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The bulk moduli of ethanol, mercury and water are given as $0.9, 25$ and $2 .2$ respectively in units of $10^9\, Nm^{-2}$ . For a given value of pressure, the fractional compression in volume is $\frac{{\Delta V}}{V}$. Which of the following statements about $\frac{{\Delta V}}{V}$ for these three liquids is correct ?
The density and breaking stress of a wire are $6 \times$ $10^4 \mathrm{~kg} / \mathrm{m}^3$ and $1.2 \times 10^8 \mathrm{~N} / \mathrm{m}^2$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $\frac{1^{\text {rd }}}{3}$ of the value on the surface of earth. The maximum length of the wire with breaking is ............ $\mathrm{m}$ (take, $\mathrm{g}=$ $\left.10 \mathrm{~m} / \mathrm{s}^2\right)$
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
A pendulum consisting of a small sphere of mass $m$ suspended by an inextensible and massless string of length $l$ is made to swing in a vertical plane. If the breaking strength of the string is $2mg$ , then the maximum angular amplitude of the displacement from the vertical can be ....... $^o$
An iron rod of length $2m$ and cross section area of $50\,m{m^2}$, stretched by $0.5\, mm$, when a mass of $250\, kg$ is hung from its lower end. Young's modulus of the iron rod is