Copper has a face-centered cubic $(fcc)$ lattice with an interatomic spacing equal to $2.54 \ \mathring{A}$. The value of the lattice constant for this lattice is .... $\mathring{A}$ $[AIPMT \ 2005]$

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

$A$ sphere of mass $4 \,kg$ is attached to one end of a steel wire of length $1 \,m$ and radius $1 \,mm$. It is whirled in a vertical circle with an angular velocity $10 \,rad \,s^{-1}$. If the sphere is at the lowest point of its path,the elongation in the wire is . . . . . . $(g=10 \,ms^{-2}, Y_{\text{steel}}=20 \times 10^{10} \,Nm^{-2})$ (in $\,mm$)

$A$ 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 $v$.

The maximum possible height of a mountain on Earth is approximately (elastic limit of mountain rock $= 30 \times 10^7 \ N m^{-2}$,average density of mountain rock $= 3 \times 10^3 \ kg m^{-3}$,$g = 10 \ m s^{-2}$). (in $km$)

An elevator cable can have a maximum stress of $7 \times 10^7\,N/m^2$ for appropriate safety factors. Its maximum upward acceleration is $1.5\,m/s^2$. If the cable has to support the total weight of $2000\,kg$ of a loaded elevator,the minimum area of cross-section of the cable should be ....... $cm^2$ $(g = 10\,m/s^2)$.