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 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
Zero
- B
$\frac {mgL}{2AY}$
- C
$\frac {mgL}{AY}$
- D
$\frac {2mgL}{AY}$
Similar Questions
When a uniform wire of radius $r$ is stretched by a $2kg$ weight, the increase in its length is $2.00\, mm$. If the radius of the wire is $r/2$ and other conditions remain the same, the increase in its length is .......... $mm$
When a uniform wire of radius $r$ is stretched by a $2kg$ weight, the increase in its length is $2.00\, mm$. If the radius of the wire is $r/2$ and other conditions remain the same, the increase in its length is .......... $mm$
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, $Y_{\text {steel }}=20 \times 10^{11} \,dyne / cm ^2$, $Y_{\text {copper }}=12 \times 10^{11} \,dyne / cm ^2$
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, $Y_{\text {steel }}=20 \times 10^{11} \,dyne / cm ^2$, $Y_{\text {copper }}=12 \times 10^{11} \,dyne / cm ^2$
Column$-II$ is related to Column$-I$. Join them appropriately :
Column $-I$
Column $-II$
$(a)$ When temperature raised Young’s modulus of body
$(i)$ Zero
$(b)$ Young’s modulus for air
$(ii)$ Infinite
$(iii)$ Decreases
$(iv)$Increases
Column$-II$ is related to Column$-I$. Join them appropriately :
| Column $-I$ | Column $-II$ |
| $(a)$ When temperature raised Young’s modulus of body | $(i)$ Zero |
| $(b)$ Young’s modulus for air | $(ii)$ Infinite |
| $(iii)$ Decreases | |
| $(iv)$Increases |
The Young's modulus of a steel wire of length $6\,m$ and cross-sectional area $3\,mm ^2$, is $2 \times 11^{11}\,N / m ^2$. The wire is suspended from its support on a given planet. A block of mass $4\,kg$ is attached to the free end of the wire. The acceleration due to gravity on the planet is $\frac{1}{4}$ of its value on the earth. The elongation of wire is (Take $g$ on the earth $=10$ $\left.m / s ^2\right):$
The Young's modulus of a steel wire of length $6\,m$ and cross-sectional area $3\,mm ^2$, is $2 \times 11^{11}\,N / m ^2$. The wire is suspended from its support on a given planet. A block of mass $4\,kg$ is attached to the free end of the wire. The acceleration due to gravity on the planet is $\frac{1}{4}$ of its value on the earth. The elongation of wire is (Take $g$ on the earth $=10$ $\left.m / s ^2\right):$
- [JEE MAIN 2023]
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:
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:
- [JEE MAIN 2021]