A wire is stretched by $0.01$ $m$ by a certain force $F.$ Another wire of same material whose diameter and length are double to the original wire is stretched by the same force. Then its elongation will be
Medium
Download our app for free and get started
(a) $l = \frac{{FL}}{{\pi {r^2}Y}}$
$l \propto \frac{L}{{{r^2}}}$ $(Y$ and $F$ are constant$)$
$\frac{{{l_2}}}{{{l_1}}} = \frac{{{L_2}}}{{{L_1}}} \times {\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2} = (2) \times {\left( {\frac{1}{2}} \right)^2} = \frac{1}{2}$
==> ${l_2} = \frac{{{l_1}}}{2} = \frac{{0.01m}}{2} = 0.005m$
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 upper end of a wire of radius $4\, mm$ and length $100\, cm$ is clamped and its other end is twisted through an angle of $60^o$. Then angle of shear is .......... $^o$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
- 3View SolutionWhen compared with solids and liquids, the gases have
- 4A steel wire is stretched with a definite load. If the Young's modulus of the wire is $Y$. For decreasing the value of $Y$View Solution
- 5A rubber pipe of density $1.5 \times {10^3}\,N/{m^2}$ and Young's modulus $5 \times {10^6}\,N/{m^2}$ is suspended from the roof. The length of the pipe is $8 \,m$. What will be the change in length due to its own weightView Solution
- 6Two blocks of masses $3 \,{kg}$ and $5\, {kg}$ are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{24}{\pi} \times 10^{2}\, {Nm}^{-2}$. What is the minimum radius of the wire? (Take $\left.g=10\, {ms}^{-2}\right)$ (in $cm$)View Solution
- 7A 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
- 8Young’s moduli of two wires $A$ and $B$ are in the ratio $7 : 4$. Wire $A$ is $2\, m$ long and has radius $R$. Wire $A$ is $2\, m$ long and has radius $R$. Wire $B$ is $1.5\, m$ long and has radius $2\, mm$. If the two wires stretch by the same length for a given load, then the value of $R$ is close to ......... $mm$View Solution
- 9View SolutionFour uniform wires of the same material are stretched by the same force. The dimensions of wire are as given below. The one which has the minimum elongation has
- 10View SolutionModulus of rigidity of a liquid