Under the elastic limit,the stress is:

The length of a rod under longitudinal tension $T_1$ is $L_1$ and that under longitudinal tension $T_2$ is $L_2$. What is the actual length of the rod,in the absence of tensions?

$A$ composite heavy rope made of two materials is suspended vertically from a high ceiling. The ratios of different quantities for the upper rope to the lower rope are: length $\frac{L_u}{L_l} = \frac{1}{2}$,cross-sectional area $\frac{A_u}{A_l} = \frac{2}{1}$,and density $\frac{d_u}{d_l} = \frac{2}{3}$. What is the ratio of the maximum stress in the two ropes?

The elastic limit for a gas

Match List-$I$ with List-$II$ :

List-$I$	List-$II$
$(A)$ $A$ force that restores an elastic body of unit area to its original state	$(I)$ Bulk modulus
$(B)$ Two equal and opposite forces parallel to opposite faces	$(II)$ Young's modulus
$(C)$ Forces perpendicular everywhere to the surface per unit area same everywhere	$(III)$ Stress
$(D)$ Two equal and opposite force perpendicular to opposite faces	$(IV)$ Shear modulus

Choose the correct answer from the options given below:

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 $cm$)