If the length of a string is $P$ when the tension in it is $6 \ N$ and its length is $Q$ when the tension in it is $8 \ N$, then the original length of the string is

$A$ force $F$ is needed to break a copper wire having radius $R$. The force needed to break a copper wire of radius $2R$ will be

When a load of $10 \,kg$ is suspended on a metallic wire,its length increases by $2 \,mm$. The force constant of the wire is ........ $N/m$.

Consider a long steel bar under a tensile stress due to force $F$ acting at the edges along the length of the bar (as shown in figure). Consider a plane making an angle $\theta$ with the length. What are the tensile and shearing stresses on this plane?
$(a)$ For what angle is the tensile stress a maximum?
$(b)$ For what angle is the shearing stress a maximum?

Match the physical quantities in Column-$I$ with the details given in Column-$II$ appropriately:

Column-$I$	Column-$II$
$(a)$ $\text{Stress} \propto \text{Strain}$	$(i)$ $M^1 L^{-1} T^{-2}$
$(b)$ $\text{Dimensional formula for compressibility}$	$(ii)$ $M^{-1} L^1 T^2$
	$(iii)$ $\text{Poisson's ratio}$
	$(iv)$ $\text{Hooke's law}$

Which one of the following is the weakest kind of bonding in solids?