To break a wire,a breaking stress of $10^6 \, N/m^2$ is required. If the density of the material is $3 \times 10^3 \, kg/m^3$,then the length of the wire which will break by its own weight will be......... $m$ (Take $g = 10 \, m/s^2$)

$A$ 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 $= 10^{-2} \; cm^{2}$)

$A$ force $F$ is needed to break a copper wire having radius $R$. The force needed to break a copper wire of radius $2R$ will be

Mark the wrong statement.

Potassium has a $bcc$ structure with a nearest neighbour distance of $4.525 \ \mathring{A}$. Its atomic weight is $39$. Its density in $kg/m^{3}$ is:

Two blocks of masses $1 \, kg$ and $2 \, kg$ are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal is $2 \times 10^9 \, N/m^2$. What should be the minimum radius of the wire used if it is not to break? Take $g = 10 \, m/s^2$.