A wire of length $50\, cm$ and cross sectional area of $1$ sq. mm is extended by $1\, mm.$ The required work will be $(Y = 2 \times {10^{10}}\,N{m^{ - 2}})$
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Two wires $A$ and $B $ of same length and of the same material have the respective radii ${r_1}$ and ${r_2}$. Their one end is fixed with a rigid support, and at the other end equal twisting couple is applied. Then the ratio of the angle of twist at the end of $A$ and the angle of twist at the end of $B $ will be
A stone of mass $20\, {g}$ is projected from a rubber catapult of length $0.1\, {m}$ and area of cross section $10^{-6} \,{m}^{2}$ stretched by an amount $0.04\, {m}$. The velocity of the projected stone is $....\,m\,/s.$ (Young's modulus of rubber $=0.5 \times 10^{9}\, {N} / {m}^{2}$ )
Density of rubber is $d$. $ A$ thick rubber cord of length $L$ and cross-section area $A$ undergoes elongation under its own weight on suspending it. This elongation is proportional to
The pressure that has to be applied to the ends of a steel wire of length $10\ cm$ to keep its length constant when its temperature is raised by $100^o C$ is: (For steel Young's modulus is $2 \times 10^{11}$ $Nm^{-1}$ and coefficient of thermal expansion is $1.1 \times 10^{-5}$ $K^{-1}$ )
A brass rod of cross-sectional area $1\,c{m^2}$ and length $0.2\, m$ is compressed lengthwise by a weight of $5\, kg$. If Young's modulus of elasticity of brass is $1 \times {10^{11}}\,N/{m^2}$ and $g = 10\,m/{\sec ^2}$, then increase in the energy of the rod will be
Wires ${W}_{1}$ and ${W}_{2}$ are made of same material having the breaking stress of $1.25 \times 10^{9} \,{N} / {m}^{2}$ ${W}_{1}$ and ${W}_{2}$ have cross-sectional area of $8 \times 10^{-7}\, {m}^{2}$ and $4 \times 10^{-7}\, {m}^{2}$, respectively. Masses of $20 \,{kg}$ and $10\, {kg}$ hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is $.....{kg}$ (Use $\left.{g}=10\, {m} / {s}^{2}\right)$
A steel wire of diameter $2\ mm$ has a breaking strength of $4 \times 10^5 N$.the breaking force $......... \times 10^5 N$ of similar steel wire of diameter $1.5\ mm ?$
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
Two steel wires of same length but radii $r$ and $2r$ are connected together end to end and tied to a wall as shown. The force stretches the combination by $10\ mm$. How far does the midpoint $A$ move ............ $mm$