What is the percentage increase in length of a wire of diameter $2.5 \,mm$, stretched by a force of $100 \,kg$ wt is .................. $\%$ ( Young's modulus of elasticity of wire $=12.5 \times 10^{11} \,dyne / cm ^2$ )
Medium
Download our app for free and get started
(a)
$Y=\frac{F L}{A \Delta L} \Rightarrow \text { Percentage increase } \frac{\Delta L}{L} \times 100=\frac{F}{A Y} \times 100$
$\text { Diameter }=2.5 \,mm$
$d=\frac{2.5}{1000} \,m$
Area $=\frac{\pi d^2}{4} \quad Y=12.5 \times 10^{11} \,dyne / cm ^2$ $\left\{\frac{1 \text { dyne }}{ cm ^2}=\frac{0.1 \,N }{ m ^2}\right\}$
$\Rightarrow A=\frac{\pi \times(2.5)^2}{4} \quad F=100 \times 10=1000 \,N$
$\Rightarrow \frac{1000 \times L}{\frac{3.14 \times(2.5)^2}{4 \times(1000)^2} \times 12.5 \times 10^{11} \times 0.1}=\frac{\Delta L}{L} \times 100$
$=0.16 \%$
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
- 1$Assertion :$ Solids are least compressible and gases are most compressible.View Solution
$Reason :$ solids have definite shape and volume but gases do not have either definite shape or definite volume. - 2View SolutionIf the tension on a wire is removed at once, then
- 3View SolutionWhich one of the following substances possesses the highest elasticity
- 4View SolutionWhich one of the following quantities does not have the unit of force per unit area
- 5A 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
- 6A 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
- 7A meter scale of mass $m$ , Young modulus $Y$ and cross section area $A$ is hanged vertically from ceiling at zero mark. Then separation between $30\ cm$ and $70\ cm$ mark will be :-( $\frac{{mg}}{{AY}}$ is dimensionless)View Solution
- 8The force required to stretch a steel wire of $1\,c{m^2}$ cross-section to $1.1$ times its length would be $(Y = 2 \times {10^{11}}\,N{m^{ - 2}})$View Solution
- 9View SolutionIf the temperature increases, the modulus of elasticity
- 10If the Bulk modulus of lead is $8.0 \times 10^9 \,N / m ^2$ and the initial density of the lead is $11.4 \,g / cc$, then under the pressure of $2.0 \times 10^8 \,N / m ^2$, the density of the lead is $............. g / cc$View Solution