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A wire of length $5 \,m$ is twisted through $30^{\circ}$ at free end. If the radius of wire is $1 \,mm$, the shearing strain in the wire is $..........,.$
A steel wire of diameter $0.5 mm$ and Young's modulus $2 \times 10^{11} N m ^{-2}$ carries a load of mass $M$. The length of the wire with the load is $1.0 m$. A vernier scale with $10$ divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count $1.0 mm$, is attached. The $10$ divisions of the vernier scale correspond to $9$ divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by $1.2 kg$, the vernier scale division which coincides with a main scale division is. . . . Take $g =10 m s ^{-2}$ and $\pi=3.2$.
A uniform rod of mass $m$, length $L$, area of cross-section $A$ and Young's modulus $Y$ hangs from the ceiling. Its elongation under its own weight will be
A weight of $200 \,kg$ is suspended by vertical wire of length $600.5\, cm$. The area of cross-section of wire is $1\,m{m^2}$. When the load is removed, the wire contracts by $0.5 \,cm$. The Young's modulus of the material of wire will be
A rubber cord catapult has cross-sectional area $25\,m{m^2}$ and initial length of rubber cord is $10\,cm.$ It is stretched to $5\,cm.$ and then released to project a missile of mass $5gm.$ Taking ${Y_{rubber}} = 5 \times {10^8}N/{m^2}$ velocity of projected missile is ......... $ms^{-1}$
If Young's modulus of iron is $2 \times {10^{11}}\,N/{m^2}$ and the interatomic spacing between two molecules is $3 \times {10^{ - 10}}$metre, the interatomic force constant is ......... $N/m$
Auniform rod rotating in gravity free region with certain constant angular velocity. The variation of tensile stress with distance $x$ from axis of rotation is best represented by which of the following graphs.
A rod of length $L$ at room temperature and uniform area of cross section $A$, is made of a metal having coefficient of linear expansion $\alpha {/^o}C$. It is observed that an external compressive force $F$, is applied on each of its ends, prevents any change in the length of the rod, when it temperature rises by $\Delta \,TK$. Young’s modulus, $Y$, for this metal is