$A$ wire of length $5 \,m$ is twisted through $30^{\circ}$ at its free end. If the radius of the wire is $1 \,mm$,the shearing strain in the wire is: (in $^{\circ}$)

$A$ rod of length $1.05 \; m$ having negligible mass is supported at its ends by two wires of steel (wire $A$) and aluminium (wire $B$) of equal lengths as shown in Figure. The cross-sectional areas of wires $A$ and $B$ are $1.0 \; mm^{2}$ and $2.0 \; mm^{2}$ respectively. At what point along the rod should a mass $m$ be suspended in order to produce $(a)$ equal stresses and $(b)$ equal strains in both steel and aluminium wires?

Which of the following statements is incorrect?

$A$ body of mass $10 \ kg$ is attached to a wire of $0.3 \ m$ length. The breaking stress is $4.8 \times 10^7 \ N \ m^{-2}$. The area of cross-section of the wire is $10^{-6} \ m^2$. The maximum angular velocity with which it can be rotated in a horizontal circle is

$A$ man grows into a giant such that his linear dimensions increase by a factor of $9$. Assuming that his density remains the same,the stress in the leg will change by a factor of

$A$ steel wire of diameter $2 \,mm$ has a breaking strength of $4 \times 10^5 \,N$. What is the breaking force in $\times 10^5 \,N$ for a similar steel wire of diameter $1.5 \,mm$?