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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 $=0.5 \times 10^{9}\, {N} / {m}^{2}$ )
A $5\, m$ long aluminium wire ($Y = 7 \times {10^{10}}N/{m^2})$ of diameter $3\, mm$ supports a $40\, kg$ mass. In order to have the same elongation in a copper wire $(Y = 12 \times {10^{10}}N/{m^2})$ of the same length under the same weight, the diameter should now be, in $mm.$
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
Young's moduli of the material of wires $A$ and $B$ are in the ratio of $1: 4$, while its area of cross sections are in the ratio of $1: 3$. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires $A$ and $B$ will be in the ratio of
A wire is loaded by $6\, kg$ at its one end, the increase in length is $12\, mm.$ If the radius of the wire is doubled and all other magnitudes are unchanged, then increase in length will be ......... $mm$
A steel rod of length $1\,m$ and cross sectional area $10^{-4}\,m ^2$ is heated from $0^{\circ}\,C$ to $200^{\circ}\,C$ without being allowed to extend or bend. The compressive tension produced in the rod is $........\times 10^4\,N$ (Given Young's modulus of steel $=2 \times 10^{11}\,Nm ^{-2}$, coefficient of linear expansion $=10^{-5}\, K ^{-1}$.
The ratio of Young's modulus of the material of two wires is $2 : 3.$ If the same stress is applied on both, then the ratio of elastic energy per unit volume will be
A block of mass $M$ is suspended from a wire of length $L$, area of cross-section $A$ and Young's modulus $Y$. The elastic potential energy stored in the wire is