When a pressure of $100$ atmosphere is applied on a spherical ball, then its volume reduces to $0.01\%$. The bulk modulus of the material of the rubber in $dyne/c{m^2}$ is
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The breaking stress of a wire of length $L$ and radius $r$ is $5$ $kg - wt/{m^2}$. The wire of length $2l$ and radius $2r$ of the same material will have breaking stress in $kg - wt/{m^2}$
A horizontal steel railroad track has a length of $100 \,m$, when the temperature is $25^{\circ} C$. The track is constrained from expanding or bending. The stress on the track on a hot summer day, when the temperature is $40^{\circ} C$ is ............. $\times 10^7\,Pa$ (Note : The linear coefficient of thermal expansion for steel is $1.1 \times 10^{-5} /{ }^{\circ} C$ and the Young's modulus of steel is $2 \times 10^{11} \,Pa$ )
Two wires $A$ and $B$ of same length, same area of cross-section having the same Young's modulus are heated to the same range of temperature. If the coefficient of linear expansion of $A$ is $3/2$ times of that of wire $B$. The ratio of the forces produced in two wires 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 ......... $ms^{-1}$
What must be the lengths of steel and copper rods at $0^o C$ for the difference in their lengths to be $10\,cm$ at any common temperature? $(\alpha_{steel}=1.2 \times {10^{-5}} \;^o C^{-1})$ and $(\alpha_{copper} = 1.8 \times 10^{-5} \;^o C^{-1})$
Each of three blocks $P$, $Q$ and $R$ shown in figure has a mass of $3 \mathrm{~kg}$. Each of the wire $A$ and $B$ has cross-sectional area $0.005 \mathrm{~cm}^2$ and Young's modulus $2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$. Neglecting friction, the longitudinal strain on wire $B$ is____________ $\times 10^{-4}$. $\left(\right.$ Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )
A uniform cubical block is subjected to volumetric compression, which decreases its each side by $2 \%$. The Bulk strain produced in it is ............