A wire is loaded by $6\, kg$ at its one end, the increase in length is $12\, mm.$ If the radius of the wire is doubled and all other magnitudes are unchanged, then increase in length will be ......... $mm$
A$6$
B$3$
C$24$
D$48$
Easy
Download our app for free and get started
B$3$
b (b) $l \propto \frac{1}{{{r^2}}}$.
If radius of the wire is doubled then increment in length will become $\frac{1}{4}$ times i.e. $\frac{{12}}{4} = 3mm$
Download our app
and 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.*
The density of a metal at normal pressure is $\rho$. Its density when it is subjected to an excess pressure $p$ is $\rho^{\prime}$ If $B$ is Bulk modulus of the metal, the ratio of $\frac{{\rho '}}{\rho }$ is
An $8\,m$ long copper wire and $4\,m$ long steel wire, each of cross section $0.5\,cm^2$ are fastened end to end and stretched by $500\,N$ force. The elastic potential energy of the system is (Youngs mod $: Y_{cu}= 1\times 10^{11}\,N/m^2,$ $Y_{steel} = 2\times 10^{11}\,N/m^2$ ) :
There 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 be
A metal rod of cross-sectional area $10^{-4} \,m ^{2}$ is hanging in a chamber kept at $20^{\circ} C$ with a weight attached to its free end. The coefficient of thermal expansion of the rod is $2.5 \times 10^{-6} \,K ^{-1}$ and its Young's modulus is $4 \times 10^{12} \,N / m ^{2}$. When the temperature of the chamber is lowered to $T$, then a weight of $5000 \,N$ needs to be attached to the rod, so that its length is unchanged. Then, $T$ is ............ $^{\circ} C$
The area of cross-section of a railway track is $0.01\, {m}^{2}$. The temperature variation is $10^{\circ} {C}$. Coefficient of linear expansion of material of track is $10^{-5} /{ }^{\circ} {C}$. The energy stored per meter in the track is ...... ${J} / {m} .$
(Young's modulus of material of track is $10^{11} \,{Nm}^{-2}$ ))