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
A${10^{ - 5}}\,J$
B$2.5 \times {10^{ - 5}}\,J$
C$5 \times {10^{ - 5}}\,J$
D$2.5 \times {10^{ - 4}}$ $J$
Medium
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B$2.5 \times {10^{ - 5}}\,J$
b (b) $U = \frac{1}{2} \times \frac{{{{{\rm{(stress)}}}^{\rm{2}}}}}{Y} \times {\rm{volume}}$$=$ $\frac{1}{2} \times \frac{{{F^2} \times A \times L}}{{{A^2} \times Y}}$
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Two persons pull a wire towards themselves. Each person exerts a force of $200 \mathrm{~N}$ on the wire. Young's modulus of the material of wire is $1 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$. Original length of the wire is $2 \mathrm{~m}$ and the area of cross section is $2 \mathrm{~cm}^2$. The wire will extend in length by . . . . . . . .$\mu \mathrm{m}$.
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 $\left.{g}=10\, {m} / {s}^{2}\right)$
Wires $A$ and $B$ are connected with blocks $P$ and $Q$ as shown. The ratio of lengths, radii and Young's modulus of wires $A$ and $B$ are $r, 2r$ and $3r$ respectively ($r$ is a constant). Find the mass of block $P$ if ratio of increase in their corresponding lengths is $1/6r^2$. The mass of block $Q$ is $3M$.
In plotting stress versus strain curves for two materials $P$ and $Q$, a student by mistake puts strain on the $y$-axis and stress on the $x$-axis as shown in the figure. Then the correct statement$(s)$ is(are)
$(A)$ $P$ has more tensile strength than $Q$
$(B)$ $P$ is more ductile than $Q$
$(C)$ $P$ is more brittle than $Q$
$(D)$ The Young's modulus of $P$ is more than that of $Q$
A rod of uniform cross-sectional area $A$ and length $L$ has a weight $W$. It is suspended vertically from a fixed support. If Young's modulus for rod is $Y$, then elongation produced in rod is ......
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