The density of a metal at normal pressure is $\rho$. Its density when it is subjected to an excess pressure$p$ is $\rho \text{'}$. If $B$ is Bulk modulus of the metal, the ratio of $\frac{\rho \text{'}}{\rho }$ is: 
 

The two blocks $P$ and $Q$ are connected by a metal wire with breaking stress ${10}^9 \mathrm{N} {\mathrm{m}}^{-2}$ through a frictionless pulley. The minimum radius of the wire for it not to break is (consider $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A mild steel wire of length $2 L$ and cross-sectional area $A$ is stretched, well with in the elastic limit, horizontally between two pillars as shown in figure. A mass $m$ is suspended from the mid-point of the wire. Strain in the wire is

Two blocks of masses $3 \mathrm{kg}$ and $5 \mathrm{kg}$ are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{24}{\pi }\times {10}^2 \mathrm{N} {\mathrm{m}}^{-2}$. What is the minimum radius of the wire ?
( take $\left.g=10{ \mathrm{m} \mathrm{s}}^{-2}\right)$