A wire of cross sectional area $A$, modulus of elasticity $2 \times 10^{11} \mathrm{Nm}^{-2}$ and length $2 \mathrm{~m}$ is stretched between two vertical rigid supports. When a mass of $2 \mathrm{~kg}$ is suspended at the middle it sags lower from its original position making angle $\theta=\frac{1}{100}$ radian on the points of support. The value of $A$ is. . . . . . $\times 10^{-4} \mathrm{~m}^2$ (consider $\mathrm{x}<\mathrm{L}$ ).
(given: $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )
JEE MAIN 2024, Diffcult
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 wire of diameter $1mm$ breaks under a tension of $1000\, N.$ Another wire, of same material as that of the first one, but of diameter $2\, mm$ breaks under a tension of ...... $N$View Solution
- 2Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is $1: 4,$ the ratio of their diameters isView Solution
- 3A steel wire of diameter $0.5 mm$ and Young's modulus $2 \times 10^{11} N m ^{-2}$ carries a load of mass $M$. The length of the wire with the load is $1.0 m$. A vernier scale with $10$ divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count $1.0 mm$, is attached. The $10$ divisions of the vernier scale correspond to $9$ divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by $1.2 kg$, the vernier scale division which coincides with a main scale division is. . . . Take $g =10 m s ^{-2}$ and $\pi=3.2$.View Solution
- 4A steel wire can sustain $100\,kg$ weight without breaking. If the wire is cut into two equal parts, each part can sustain a weight of ......... $kg$View Solution
- 5The 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
- 6The elastic limit of brass is $379\,MPa.$ .......... $mm$ should be the minimum diameter of a brass rod if it is to support a $400\,N$ load without exceeding its elastic limit .View Solution
- 7View SolutionThere is no change in the volume of a wire due to change in its length on stretching. The poisson's ratio of the material of the wire is
- 8A composite heavy rope of two materials is suspended vertically from a high ceiling. The ratios of different quantities for upper to lower rope are length $\frac{{{L_u}}}{{{L_l}}} = \frac{1}{2}$ , cross sectional area $\frac{{{A_u}}}{{{A_l}}} = \frac{2}{1}$ ,density $\frac{{{d_u}}}{{{d_l}}} = \frac{2}{3}$ .What is the ratio of maximum stress in the two ropesView Solution
- 9A rod $BC$ of negligible mass fixed at end $B$ and connected to a spring at its natural length having spring constant $K = 10^4\ N/m$ at end $C$, as shown in figure. For the rod $BC$ length $L = 4\ m$, area of cross-section $A = 4 × 10^{-4}\ m^2$, Young's modulus $Y = 10^{11} \ N/m^2$ and coefficient of linear expansion $\alpha = 2.2 × 10^{-4} K^{-1}.$ If the rod $BC$ is cooled from temperature $100^oC$ to $0^oC,$ then find the decrease in length of rod in centimeter.(closest to the integer)View Solution
- 10A steel rod has a radius $10 \,mm$ and a length of $1.0 \,m$. A force stretches it along its length and produces a strain of $0.32 \%$. Young's modulus of the steel is $2.0 \times 10^{11} \,Nm ^{-2}$. What is the magnitude of the force stretching the rod is ........ $kN$View Solution