The dimensional formula for the modulus of rigidity is

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 ..... $^\circ$.

$A$ rod of length $l$ and radius $r$ is joined to a rod of length $l/2$ and radius $r/2$ of the same material. The free end of the small rod is fixed to a rigid base,and the free end of the larger rod is given a twist of $\theta^\circ$. The twist angle at the joint will be:

Two wires of the same length and same material have radii $r_1$ and $r_2$. Their one end is fixed,and when an equal torque is applied to the other end,what is the ratio of their angular displacement?

The upper end of a wire of diameter $12\,mm$ and length $1\,m$ is clamped and its other end is twisted through an angle of $30^{\circ}$. The angle of shear is $........^{\circ}$.

$A$ square lead slab of side $50\, cm$ and thickness $10\, cm$ is subject to a shearing force (on its narrow face) of $9.0 \times 10^{4} \, N$. The lower edge is riveted to the floor. How much will the upper edge be displaced? (Given: Shear modulus of lead $G = 5.6 \times 10^{9} \, N/m^2$)