Copper of fixed volume $V$ is drawn into wire of length $l$. When this wire is subjected to a constant force $F$, the extension produced in the wire is $\Delta l$. Which of the following graphs is a straight line?
AIPMT 2014, Easy
Download our app for free and get started
As $V=Al$ $.....(i)$
where $A$ is the area of $cross-section$ of the wire.
$Young's\,modulus,\,Y = \frac{{\left( {F/A} \right)}}{{\left( {\Delta l/l} \right)}} = \frac{{Fl}}{{A\Delta l}}$
$\Delta l = \frac{{Fl}}{{YA}} = \frac{{F{l^2}}}{{YV}}$ $(Using(i))$
$\Delta l \propto {l^2}$
Hence, the graph between $\Delta l$ and ${l^2}$ is a straight line.
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 material has Poisson's ratio $0.5$. If a uniform rod of it suffers a longitudinal strain of $3 \times 10^{-3}$, what will be percentage increase in volume is .......... $\%$View Solution
- 2Under the same load, wire $A$ having length $5.0\,m$ and cross section $2.5 \times 10^{-5}\,m ^2$ stretches uniformly by the same amount as another wire $B$ of length $6.0\,m$ and a cross section of $3.0 \times 10^{-5}\,m ^2$ stretches. The ratio of the Young's modulus of wire $A$ to that of wire $B$ will beView Solution
- 3An increases in pressure required to decreases the $200\,litres$ volume of a liquid by $0.004\%$ in container is ............ $kPa$ (Bulk modulus of the liquid $= 2100\,MPa$ )View Solution
- 4The Young's modulus of a wire of length $L$ and radius $r$ is $Y$ $N/m^2$. If the length and radius are reduced to $L/2$ and $r/2,$ then its Young's modulus will beView Solution
- 5Two 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
- 6View SolutionWhich of the following statements is correct
- 7A wire of length $2\, m$ is made from $10\;c{m^3}$ of copper. A force $F$ is applied so that its length increases by $2\, mm.$ Another wire of length 8 m is made from the same volume of copper. If the force $F$ is applied to it, its length will increase by......... $cm$View Solution
- 8In an experiment to determine the Young's modulus, steel wires of five different lengths $(1,2,3,4$ and $5\,m )$ but of same cross section $\left(2\,mm ^{2}\right)$ were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is $x \times 10^{11}\,Nm ^{-2}$, then the value of $x$ isView Solution
- 9View SolutionThe substances having very short plastic region are
- 10View SolutionWhich of the following relations is true