$A$ cube of aluminium of sides $0.1 \, m$ is subjected to a shearing force of $100 \, N$. The top face of the cube is displaced through $0.02 \, cm$ with respect to the bottom face. The shearing strain would be

Two blocks of masses $3 \, kg$ and $5 \, kg$ are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{24}{\pi} \times 10^{2} \, Nm^{-2}$. What is the minimum radius of the wire? (Take $g = 10 \, ms^{-2}$) (in $cm$)

The elastic limit of brass is $3.5 \times 10^{10} \, N/m^2$. Find the maximum load that can be applied to a brass wire of $0.75 \, mm$ diameter without exceeding the elastic limit $....... \times 10^4 \, N$.

Hooke's law defines:

The length of a metal wire is $l_{1}$ when the tension in it is $T_{1}$,and it is $l_{2}$ when the tension is $T_{2}$. The natural length of the wire is -

Why do spring balances show wrong readings of weight after they have been used for a long time?