Wires $A$ and $B$ are made from the same material. $A$ has twice the diameter and three times the length of $B.$ If the elastic limits are not reached, when each is stretched by the same tension, the ratio of energy stored in $A$ to that in $B$ is
A$2:3$
B$3:4$
C$3:2$
D$6:1$
Medium
Download our app for free and get started
B$3:4$
b (b) $U = \frac{1}{2}Fl = \frac{{{F^2}L}}{{2AY}}$. $U \propto \frac{L}{{{r^2}}}$ $(F$ and $Y$ are constant$)$
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.*
Four identical hollow cylindrical columns of mild steel support a big structure of mass $50 \times 10^{3} {kg}$, The inner and outer radii of each column are $50\; {cm}$ and $100 \;{cm}$ respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use $\left.{Y}=2.0 \times 10^{11} \;{Pa}, {g}=9.8\; {m} / {s}^{2}\right]$
The elongation of a wire on the surface of the earth is $10^{-4} \; m$. The same wire of same dimensions is elongated by $6 \times 10^{-5} \; m$ on another planet. The acceleration due to gravity on the planet will be $\dots \; ms ^{-2}$. (Take acceleration due to gravity on the surface of earth $=10 \; m / s ^{-2}$ )
A steel wire is $1 \,m$ long and $1 \,mm ^2$ in area of cross$-$section. If it takes $200 \,N$ to stretch this wire by $1 \,mm$, how much force will be required to stretch a wire of the same material as well as diameter from its normal length of $10 \,m$ to a length of $1002 \,cm$ is $........ N$
A 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 .......... $\%$