$A$ 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 $^{\circ}$)

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.

$A$ 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

Two identical steel cubes (masses $50\,g$,side $1\,cm$) collide head-on face to face with a speed of $10\,cm/s$ each. Find the maximum compression of each. Young's modulus for steel $Y = 2 \times 10^{11}\,N/m^2$.

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

$A$ bob of mass $10\, kg$ is attached to a wire $0.3\, m$ long. Its 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 ....... $rad/sec$.