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
$4 \times {10^5}$
$1 \times {10^5}$
$2 \times {10^5}$
$1 \times {10^4}$
Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are $Y_{1}$ and $Y_{2}$. The combination behaves as a single wire then its Young's modulus 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 steel rod has a radius $10 \,mm$ and a length of $1.0 \,m$. A force stretches it along its length and produces a strain of $0.32 \%$. Young's modulus of the steel is $2.0 \times 10^{11} \,Nm ^{-2}$. What is the magnitude of the force stretching the rod is ........ $kN$
A brass rod of length $2\,m$ and cross-sectional area $2.0\,cm^2$ is attached end to end to a steel rod of length $L$ and cross-sectional area $1.0\,cm^2$ . The compound rod is subjected to equal and opposite pulls of magnitude $5 \times 10^4\,N$ at its ends. If the elongations of the two rods are equal, then length of the steel rod $(L)$ is ........... $m$ $(Y_{Brass}=1.0\times 10^{11}\,N/m^2$ and $Y_{Steel} = 2.0 \times 10^{11}\,N/m^2)$
Two wires each of radius $0.2\,cm$ and negligible mass, one made of steel and other made of brass are loaded as shown in the figure. The elongation of the steel wire is $.........\times 10^{-6}\,m$. [Young's modulus for steel $=2 \times 10^{11}\,Nm ^{-2}$ and $g =10\,ms ^{-2}$ ]