$A$ substance breaks down by a stress of $10^6 \ N/m^2$. If the density of the material of the wire is $3 \times 10^3 \ kg/m^3$,then the length of the wire of the substance which will break under its own weight when suspended vertically,is ......... $m$.

If the breaking force for a given wire is $F$, and the thickness of the wire is doubled, then the breaking force will be:

One end of a steel wire is fixed to the ceiling of an elevator moving up with an acceleration $2 \ m/s^2$ and a load of $10 \ kg$ hangs from the other end. If the cross-section of the wire is $2 \ cm^2$,then the longitudinal strain in the wire will be ($g = 10 \ m/s^2$ and $Y = 2.0 \times 10^{11} \ N/m^2$).

Two blocks of masses $1 \, kg$ and $2 \, kg$ are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal is $2 \times 10^9 \, N/m^2$. What should be the minimum radius of the wire used if it is not to break? Take $g = 10 \, m/s^2$.

$A$ steel wire is suspended vertically from a rigid support. When loaded with a weight in air,it extends by $l_a$ and when the weight is immersed completely in water,the extension is reduced to $l_w$. Then the relative density of the material of the weight is

$A$ metal wire of length $0.5\; m$ and cross-sectional area $10^{-4}\; m^{2}$ has a breaking stress of $5 \times 10^{8}\; N/m^{2}$. $A$ block of mass $10\; kg$ is attached to one end of the wire and is rotated in a horizontal circle. The maximum linear velocity of the block will be $v\; m/s$. Find $v$.