Density of rubber is $d$. $ A$ thick rubber cord of length $L$ and cross-section area $A$ undergoes elongation under its own weight on suspending it. This elongation is proportional to
A$dL$
B$Ad/L$
C$Ad/{L^2}$
D$d{L^2}$
Medium
Download our app for free and get started
D$d{L^2}$
d (d) Increment in length $l = \frac{{{L^2}dg}}{{2Y}}$ $\therefore$ $l \propto {L^2}d$
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
A rubber cord $10\, m$ long is suspended vertically. How much does it stretch under its own weight $($Density of rubber is $1500\, kg/m^3, Y = 5×10^8 N/m^2, g = 10 m/s^2$$)$
A student plots a graph from his reading on the determination of Young’s modulus of a metal wire but forgets to label. The quantities on $X$ and $Y$ axes may be respectively.
The area of cross section of the rope used to lift a load by a crane is $2.5 \times 10^{-4} m ^{2}$. The maximum lifting capacity of the crane is $10$ metric tons. To increase the lifting capacity of the crane to $25$ metric tons, the required area of cross section of the rope should be.$.........\times 10^{-4} \,m ^{2}$ (take $g =10\, ms ^{-2}$ )
A cube of aluminium of sides $0.1\, m$ is subjected to a shearing force of $100\, N$. The top face of the cube is displaced through $0.02 \,cm$ with respect to the bottom face. The shearing strain would be
Three bars having length $l, 2l$ and $3l$ and area of cross-section $A, 2 A$ and $3 A$ are joined rigidly end to end. Compound rod is subjected to a stretching force $F$. The increase in length of rod is (Young's modulus of material is $Y$ and bars are massless)
Two exactly similar wires of steel and copper are stretched by equal forces. If the total elongation is $2 \,cm$, then how much is the elongation in steel and copper wire respectively? Given, $Y_{\text {steel }}=20 \times 10^{11} \,dyne / \ cm ^2$, $Y_{\text {copper }}=12 \times 10^{11} \,dy ne / \ cm ^2$
A steel wire of length $3.2 m \left( Y _{ S }=2.0 \times 10^{11}\,Nm ^{-2}\right)$ and a copper wire of length $4.4\,M$ $\left( Y _{ C }=1.1 \times 10^{11}\,Nm ^{-2}\right)$, both of radius $1.4\,mm$ are connected end to end. When stretched by a load, the net elongation is found to be $1.4\,mm$. The load applied, in Newton, will be. (Given $\pi=\frac{22}{7}$)