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The work per unit volume to stretch the length by $1\%$ of a wire with cross sectional area of $1\,m{m^2}$ will be. $[Y = 9 \times {10^{11}}\,N/{m^2}]$
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 $=0.5 \times 10^{9}\, {N} / {m}^{2}$ )
When a weight of $10\, kg$ is suspended from a copper wire of length $3$ metres and diameter $0.4\, mm,$ its length increases by $2.4\, cm$. If the diameter of the wire is doubled, then the extension in its length will be ........ $cm$
A square aluminium (shear modulus is $25 \times 10^{9}\,Nm ^{-2}$ ) slab of side $60\,cm$ and thickness $15\,cm$ is subjected to a shearing force (on its narrow face) of $18.0 \times 10^{4}\,N$. The lower edge is riveted to the floor. The displacement of the upper edge is $.......\mu\,m$.
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 ?
A meter scale of mass $m$ , Young modulus $Y$ and cross section area $A$ is hanged vertically from ceiling at zero mark. Then separation between $30\ cm$ and $70\ cm$ mark will be :-( $\frac{{mg}}{{AY}}$ is dimensionless)
A cube of aluminium of sides $0.1\, m$ is subjected to a shearing force of $100\, N$. The top face of the cube is displaced through $0.02 \,cm$ with respect to the bottom face. The shearing strain would be
When a certain weight is suspended from a long uniform wire, its length increases by one $cm$. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one, the increase in length will be ......... $cm$