$A$ 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 length of a wire is reduced to half,then it can hold the ......... load.

In the given figure,two elastic rods $A$ and $B$ are rigidly joined to end supports. $A$ small mass $m$ is moving with velocity $v$ between the rods. All collisions are assumed to be elastic and the surface is frictionless. The time period of the small mass $m$ will be: [Here,an elastic rod may be treated as a spring of spring constant $k = \frac{YA}{L}$]

In order to determine the Young's Modulus of a wire of radius $0.2 \, cm$ (measured using a scale of least count $= 0.001 \, cm$) and length $1 \, m$ (measured using a scale of least count $= 1 \, mm$),a weight of mass $1 \, kg$ (measured using a scale of least count $= 1 \, g$) was hanged to get the elongation of $0.5 \, cm$ (measured using a scale of least count $= 0.001 \, cm$). What will be the fractional error in the value of Young's Modulus determined by this experiment? (in $\%$)

$A$ light rod of length $200\,cm$ is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and has a cross-section of $0.1\,cm^2$,and the other is made of brass with a cross-section of $0.2\,cm^2$. At what distance from the steel wire should a weight be hung along the rod to produce equal stresses in both wires?

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 $Y = 2.0 \times 10^{11} \ N/m^2$).