The length of wire, when $M_1$ is hung from it, is $I_1$ and is $I_2$ with both $M_1$ and $M_2$ hanging. The natural length of wire is ........
Diffcult
Download our app for free and get started
(a)
Let the natural length of wire be $=1$
When only $M_1$ hanging
Using $\Delta l=\frac{F L}{A Y}$
$\left(l_1-l \right)=\frac{M_1 g \cdot l}{A Y \ldots(1)}$
When both $M_1, M_2$ hanging
$\left(l_2-l\right)=\frac{\left(M_1+M_2\right) g \cdot l}{A Y} \ldots(2)$
Dividing $(1)$ by $(2)$
$\frac{l_1-l}{l_2-l}=\frac{M_1}{M_1+M_2}$
Solving this we get
$I=\frac{M_1}{M_2}\left(l_1-l_2\right)+I_1$
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 diagram shows a force-extension graph for a rubber band. Consider the following statementsView Solution
$I.$ It will be easier to compress this rubber than expand it
$II.$ Rubber does not return to its original length after it is stretched
$III.$ The rubber band will get heated if it is stretched and released
Which of these can be deduced from the graph
- 2The Poisson's ratio of a material is $0.5$. If a force is applied to a wire of this material, there is a decrease in the cross-sectional area by $4 \%$. The percentage increase in the length is ........ $\%$View Solution
- 3A rod of length $L$ at room temperature and uniform area of cross section $A$, is made of a metal having coefficient of linear expansion $\alpha {/^o}C$. It is observed that an external compressive force $F$, is applied on each of its ends, prevents any change in the length of the rod, when it temperature rises by $\Delta \,TK$. Young’s modulus, $Y$, for this metal isView Solution
- 4A rod of length $l$ and radius $r$ is joined to a rod of length $l/2$ and radius $r/2$ of same material. The free end of small rod is fixed to a rigid base and the free end of larger rod is given a twist of $\theta°$, the twist angle at the joint will beView Solution
- 5View SolutionUnder elastic limit the stress is
- 6If the interatomic spacing in a steel wire is $3.0Å$ and ${Y_{steel}}$= $20 \times {10^{10}}N/{m^2}$ then force constant isView Solution
- 7A bar of cross-sectional area $A$ is subjected two equal and opposite tensile forces at its ends as shown in figure. Consider a plane $BB'$ making an angle $\theta $ with the length The ratio of tensile stress to the shearing stress on the plane $BB'$ isView Solution
- 8View SolutionHook's law defines
- 9View SolutionIf the tension on a wire is removed at once, then
- 10View SolutionOn stretching a wire, the elastic energy stored per unit volume is