One end of a wire of $8 \,mm$ radius and $100 \,cm$ length is fixed and the other end is twisted through an angle of $45^{\circ}$. The angle of shear is (in $^{\circ}$)

$A$ string of cross-sectional area $4 \times 10^{-6} \, m^{2}$ and length $0.5 \, m$ is connected to a rigid body of mass $2 \, kg$. The body is rotated in a vertical circular path of radius $0.5 \, m$. The body acquires a speed of $5 \, m/s$ at the bottom of the circular path. The strain produced in the string when the body is at the bottom of the circle is $\dots \times 10^{-5}$. (Use Young's modulus $Y = 10^{11} \, N/m^{2}$ and $g = 10 \, m/s^{2}$)

If the length of a wire is reduced to half,then it can hold the ......... load.

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 $Y = 2 \times 10^{11}\,N/m^2$.

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.

$A$ spring is stretched by applying a load to its free end. The strain produced in the spring is