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

Two wires $A$ and $B$ having same length and material are stretched by the same force. Their diameters are in the ratio $1: 3$. The ratio of energy density of wire $A$ to that of wire $B$ when stretched,is (in $: 1$)

$A$ wire of length $1 \, m$ and Young's modulus $Y = 2.0 \times 10^{11} \, N/m^2$ is fixed between two rigid supports. If its temperature is increased by $100 ^\circ C$,what is the energy stored in the wire? (Given: $\alpha = 18 \times 10^{-6} \, ^\circ C^{-1}$,$A = 1 \, cm^2$)

Energy stored per unit volume in a stretched wire having Young's modulus $Y$ and stress $S$ is ...........

Two 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 is

One end of a slack wire (Young's modulus $Y$,length $L$ and cross-sectional area $A$) is clamped to a rigid wall and the other end to a block (mass $m$),which rests on a smooth horizontal plane. The block is set in motion with a speed $v$. What is the maximum distance the block will travel after the wire becomes taut?