$A$ metal wire of length $0.5\; m$ and cross-sectional area $10^{-4}\; m^{2}$ has a breaking stress of $5 \times 10^{8}\; N/m^{2}$. $A$ block of mass $10\; kg$ is attached to one end of the wire and is rotated in a horizontal circle. The maximum linear velocity of the block will be $v\; m/s$. Find $v$.

If the breaking force for a given wire is $F$, and the thickness of the wire is doubled, then the breaking force will be:

To break a wire,a breaking stress of $10^6 \, N/m^2$ is required. If the density of the material is $3 \times 10^3 \, kg/m^3$,then the length of the wire which will break by its own weight will be......... $m$ (Take $g = 10 \, m/s^2$)

Statement $(A)$ For an ideal liquid,the bulk modulus is infinite and the shear modulus is zero.
Statement $(B)$ The volume contraction of a metal cube of bulk modulus $140 \text{ GPa}$ and side length $10 \text{ cm}$,when subjected to a hydraulic pressure of $7 \times 10^6 \text{ Pa}$,is $-0.05 \text{ m}^3$.
Statement $(C)$ $A$ spiral spring is stretched by a weight attached to it. The strain is tensile.

Match the type of elasticity involved:

System	Type of Elasticity
$(i)$ Suspension fibre of galvanometer	$(a)$ Linear
$(ii)$ Bending of beam	$(b)$ Shear
$(iii)$ Cutting piece of paper	$(c)$ Bulk
$(iv)$ Mechanical waves in fluid	$(d)$ Shear

$A$ uniform wire of length $l$ and weight $w$ is suspended from the roof with a weight $W$ attached at the other end. The stress in the wire at a distance $l/3$ from the top is given by $(\frac{W}{A} + \gamma \frac{w}{A})$, where $A$ is the cross-sectional area of the wire. The value of $\gamma$ is . . . . . . .