An area of cross-section of rubber string is $2\,c{m^2}$. Its length is doubled when stretched with a linear force of $2 \times {10^5}$dynes. The Young's modulus of the rubber in $dyne/c{m^2}$ will be
$4 \times {10^5}$
$1 \times {10^5}$
$2 \times {10^5}$
$1 \times {10^4}$
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 $\pi=3.2$.
If Young's modulus for a material is zero, then the state of material should be
A mild steel wire of length $2l$ meter cross-sectional area $A \;m ^2$ is fixed horizontally between two pillars. A small mass $m \;kg$ is suspended from the mid point of the wire. If extension in wire are within elastic limit. Then depression at the mid point of wire will be .............
A wooden wheel of radius $R$ is made of two semicircular part (see figure). The two parts are held together by a ring made of a metal strip of cross section area $S$ and length $L$. $L$ is slighly less than $2\pi R$. To fit the ring on the wheel, it is heated so that its temperature rises by $\Delta T$ and it just steps over the wheel.As it cools down to surronding temperature, it presses the semicircular parts together. If the coefficint of linear expansion of the metal is $\alpha$, and its young's modulus is $Y$, the force that one part of wheel applies on the other part is
A wire of cross-sectional area $3\,m{m^2}$ is first stretched between two fixed points at a temperature of $20°C$. Determine the tension when the temperature falls to $10°C$. Coefficient of linear expansion $\alpha = {10^{ - 5}} { ^\circ}{C^{ - 1}}$ and $Y = 2 \times {10^{11}}\,N/{m^2}$ ........ $N$