Two blocks of mass $2 \mathrm{~kg}$ and $4 \mathrm{~kg}$ are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is $4.0 \times 10^{-5}$ $\mathrm{m}$ and Young's modulus of the metal is $2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$. The longitudinal strain developed in the wire is $\frac{1}{\alpha \pi}$. The value of $\alpha$ is [Use $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )
JEE MAIN 2024, Diffcult
Download our app for free and get started
$\mathrm{T}=\left(\frac{2 \mathrm{~m}_1 \mathrm{~m}_2}{\mathrm{~m}_1+\mathrm{m}_2}\right) \mathrm{g}=\frac{80}{3} \mathrm{~N}$
$\mathrm{~A}=\pi \mathrm{r}^2=16 \pi \times 10^{-10} \mathrm{~m}^2$
$\text { Strain }=\frac{\Delta \ell}{\ell}=\frac{\mathrm{F}}{\mathrm{AY}}=\frac{\mathrm{T}}{\mathrm{AY}}$
$=\frac{80 / 3}{16 \pi \times 10^{-10} \times 2 \times 10^{11}}=\frac{1}{12 \pi}$
$\alpha=12$
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
- 1The pressure that has to be applied to the ends of a steel wire of length $10\ cm$ to keep its length constant when its temperature is raised by $100^o C$ is: (For steel Young's modulus is $2 \times 10^{11}$ $Nm^{-1}$ and coefficient of thermal expansion is $1.1 \times 10^{-5}$ $K^{-1}$ )View Solution
- 2When load of $5\,kg$ is hung on a wire then extension of $3\,m$ takes place, then work done will be ....... $joule$View Solution
- 3Two steel wires of same length but radii $r$ and $2r$ are connected together end to end and tied to a wall as shown. The force stretches the combination by $10\ mm$. How far does the midpoint $A$ move ............ $mm$View Solution
- 4View SolutionWhich is correct relation
- 5A wire of length $5 \,m$ is twisted through $30^{\circ}$ at free end. If the radius of wire is $1 \,mm$, the shearing strain in the wire is $..........,.$View Solution
- 6If the force constant of a wire is $K,$ the work done in increasing the length of the wire by $l$ isView Solution
- 7There are two wires of same material and same length while the diameter of second wire is $2$ times the diameter of first wire, then ratio of extension produced in the wires by applying same load will beView Solution
- 8If average depth of an ocean is $4000 \mathrm{~m}$ and the bulk modulus of water is $2 \times 10^9 \mathrm{Nm}^{-2}$, then fractional compression $\frac{\Delta V}{V}$ of water at the bottom of ocean is $\alpha \times 10^{-2}$. The value of $\alpha$ is ___________(Given, $\mathrm{g}=10 \mathrm{~ms}^{-2}, \rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}$ )View Solution
- 9View SolutionThe Poisson's ratio cannot have the value
- 10The breaking stress of a wire of length $L$ and radius $r$ is $5$ $kg - wt/{m^2}$. The wire of length $2l$ and radius $2r$ of the same material will have breaking stress in $kg - wt/{m^2}$View Solution