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

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

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

$A$ string $AB$ of unstretched length $L$ is stretched by applying a force $F$ at the mid-point $C$ such that the segments $AC$ and $BC$ make an angle $\theta$ with $AB$ as shown in the figure. The string may be considered as an elastic element with a force to elongation ratio $K$. The force $F$ is given by

Two blocks of masses $1 \,kg$ and $2 \,kg$ are connected by a metal wire going over a smooth pulley. The breaking stress of metal is $\frac{40}{3 \pi} \times 10^6 \,N m^{-2}$. What should be the minimum radius of the wire used if it should not break (in $mm$)? $(g = 10 \,m s^{-2})$

For the tensile stress on the cross-section $PQRS$ to be maximum,$\theta =$ ......... $^o$