$A$ steel rod is projecting out of a rigid wall. The shearing strength of steel is $345 \, MN/m^2$. The dimensions are $AB = 5 \, cm$ and $BC = BE = 2 \, cm$. The maximum load that can be put on the face $ABCD$ is .......... $kg$ (neglect bending of the rod). Take $g = 10 \, m/s^2$.

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:

The edge of an aluminium cube is $10\; cm$ long. One face of the cube is firmly fixed to a vertical wall. $A$ mass of $100\; kg$ is then attached to the opposite face of the cube. The shear modulus of aluminium is $25\; GPa$. What is the vertical deflection of this face?

Given below are two statements: One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A)$: The stretching of a spring is determined by the shear modulus of the material of the spring.
Reason $(R)$: $A$ coil spring of copper has more tensile strength than a steel spring of same dimensions.
In the light of the above statements,choose the most appropriate answer from the options given below:

$A$ rubber cube of side $5 \ cm$ has one face fixed while a tangential force $1800 \ N$ is applied on its opposite face. If the modulus of rigidity of rubber is $2.4 \times 10^6 \ N \ m^{-2}$,then the lateral displacement of the strained face is $......$ . (in $mm$)

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 $30^\circ$. The angle of shear is ..... $^\circ$.