The Young's modulus of the material of a wire is $6 \times {10^{12}}\,N/{m^2}$ and there is no transverse strain in it, then its modulus of rigidity will be
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The Young's modulus of a wire of length $L$ and radius $r$ is $Y$. If the length is reduced to $\frac{L}{2}$ and radius is $\frac{r}{2}$ , then the Young's modulus will be
Young's modulus is determined by the equation given by $\mathrm{Y}=49000 \frac{\mathrm{m}}{\ell} \frac{\text { dyne }}{\mathrm{cm}^2}$ where $\mathrm{M}$ is the mass and $\ell$ is the extension of wre used in the experiment. Now error in Young modules $(\mathrm{Y})$ is estimated by taking data from $M-\ell$ plot in graph paper. The smallest scale divisions are $5 \mathrm{~g}$ and $0.02$ $\mathrm{cm}$ along load axis and extension axis respectively. If the value of $M$ and $\ell$ are $500 \mathrm{~g}$ and $2 \mathrm{~cm}$ respectively then percentage error of $\mathrm{Y}$ is :
A bob of mass $10\, kg$ is attached to wire $0.3\, m$ long. Its breaking stress is $4.8 \times 10^7 N/m^2$. The area of cross section of the wire is $10^{-6} m^2$. The maximum angular velocity with which it can be rotated in a horizontal circle ....... $rad/sec$
A uniform heavy rod of mass $20\,kg$. Cross sectional area $0.4\,m ^{2}$ and length $20\,m$ is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is $x \times 10^{-9} m$. The value of $x$ is
(Given. Young's modulus $Y =2 \times 10^{11} Nm ^{-2}$ અને $\left.g=10\, ms ^{-2}\right)$
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 $(\alpha_{copper} = 1.8 \times 10^{-5} \;^o C^{-1})$
The load versus elongation graphs for four wires of same length and made of the same material are shown in the figure. The thinnest wire is represented by the line
A spherical ball contracts in volume by $0.02 \%$, when subjected to a normal uniform pressure of $50$ atmosphere. The Bulk modulus of its material is ............. $Nm ^{-2}$