The Young's modulus of a steel wire of length $6\,m$ and cross-sectional area $3\,mm ^2$, is $2 \times 11^{11}\,N / m ^2$. The wire is suspended from its support on a given planet. A block of mass $4\,kg$ is attached to the free end of the wire. The acceleration due to gravity on the planet is $\frac{1}{4}$ of its value on the earth. The elongation of wire is (Take $g$ on the earth $=10$ $\left.m / s ^2\right):$
JEE MAIN 2023, Medium
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A suspended long metal wire is stretched a small distance $x$ by a load $W$ in newton suspended at the other end. Select the best answer out of the followingView Solution
- 2Two wires of copper having the length in the ratio $4 : 1$ and their radii ratio as $1 : 4$ are stretched by the same force. The ratio of longitudinal strain in the two will beView Solution
- 3A solid cube of copper of edge $10 \,cm$ subjected to a hydraulic pressure of $7 \times 10^6\, pascal$. If Bulk modulus of copper is $140 \,GPa$, then contraction in its volume will be ................ $m ^3$View Solution
- 4If one end of a wire is fixed with a rigid support and the other end is stretched by a force of $10 \,N,$ then the increase in length is $0.5\, mm$. The ratio of the energy of the wire and the work done in displacing it through $1.5\, mm$ by the weight isView Solution
- 5When a pressure of $100$ atmosphere is applied on a spherical ball, then its volume reduces to $0.01\%$. The bulk modulus of the material of the rubber in $dyne/c{m^2}$ isView Solution
- 6An aluminum rod (Young's modulus $ = 7 \times {10^9}\,N/{m^2})$ has a breaking strain of $0.2\%$. The minimum cross-sectional area of the rod in order to support a load of ${10^4}$Newton's isView Solution
- 7The compressibility of water is $6 \times 10^{-10} N ^{-1} m ^{2} .$ If one litre is subjected to a pressure of $4 \times 10^{7} Nm ^{-2}$ the decrease in its volume is (in $cc$)View Solution
- 8One end of a uniform rod of mass $m_1$ and crosssectional area $A$ is hung from a ceiling. The other end of the bar is supporting mass $m_2$. The stress at the midpoint isView Solution
- 9A uniform metal rod of $2\,\,mm^2$ cross section fixed between two walls is heated from $0\,^oC$ to $20\,^oC$ . The coefficient of linear expansion of rod is $12\,\,\times\,\,10^{-6}\,/^oC$ . Its Young's modulus of elasticity is $10^{11}\,\,N/m^2$ . The energy stored per unit volume of rod will be ....... $J/m^3$View Solution
- 10View SolutionThe following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied ?