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 ........ $N/m$.

One end of a uniform wire of length $L$ and weight $W$ is attached rigidly to a point in the roof,and a weight $W_1$ is suspended from its lower end. If $S$ is the area of cross-section of the wire,the stress in the wire at a height $3L/4$ from its lower end is

$A$ rod of constant cross-section moves towards the right with constant acceleration $a$. The graph of stress versus distance from the left end is shown in the figure. If the density of the material of the rod at cross-section $1$ is $9 \text{ g/cm}^3$,find the density at cross-section $2$ in $\text{g/cm}^3$.

$A$ 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

The elastic limit of a metal is $\frac{400}{\pi} \text{ MPa}$. If a rod of this metal is to support a $484 \text{ N}$ load without exceeding its elastic limit, the minimum diameter of the rod is: (in $\text{ mm}$)

$A$ wire can sustain a weight of $15 \, kg$. If it is cut into four equal parts,then each part can sustain a weight of ........ $kg$.