$A$ 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 $1.5 \,mm$?

Read the following two statements below carefully and state,with reasons,if it is true or false.
$(a)$ The Young's modulus of rubber is greater than that of steel;
$(b)$ The stretching of a coil is determined by its shear modulus.

$A$ 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?

$A$ body of mass $m=10 \; kg$ is attached to one end of a wire of length $L=0.3 \; m$. The maximum angular speed (in $rad \; s^{-1}$) with which it can be rotated about its other end in a space station is (Breaking stress of wire $= 4.8 \times 10^{7} \; N m^{-2}$ and area of cross-section of the wire $= 10^{-2} \; cm^{2}$)

Why is the maximum height of a mountain about $\sim 10 \ km$ on Earth?

Mark the wrong statement.