The upper end of a wire of radius $4 \, mm$ and length $100 \, cm$ is clamped and its other end is twisted through an angle of $60^o$. The angle of shear is .......... $^o$.

$A$ steel plate of face area $1 \, cm^2$ and thickness $4 \, cm$ is fixed rigidly at the lower surface. $A$ tangential force $F = 10 \, kN$ is applied on the upper surface as shown in the figure. The lateral displacement $x$ of the upper surface with respect to the lower surface is .............. $m$ (Modulus of rigidity for steel is $8 \times 10^{11} \, N/m^2$).

Two wires $A$ and $B$ of same length and of same material have radii $r_1$ and $r_2$ respectively. Their one end is fixed with a rigid support and at the other end,an equal twisting couple is applied. Then,the ratio of the angle of twist at the end of $A$ to the angle of twist at the end of $B$ will be ..............

Two wires $A$ and $B$ of the same length and of the same material have the respective radii $r_1$ and $r_2$. Their one end is fixed to a rigid support,and at the other end,an equal twisting couple is applied. The ratio of the angle of twist at the end of $A$ to the angle of twist at the end of $B$ will be:

The force required to punch a square hole of side $2\,cm$ in a steel sheet of thickness $2\,mm$ is (given: shearing stress of steel sheet $= 3.5 \times 10^8\,N/m^2$)

Steel ruptures when a shear stress of $3.5 \times 10^8 \, N \, m^{-2}$ is applied. The force needed to punch a $1 \, cm$ diameter hole in a steel sheet $0.3 \, cm$ thick is nearly: