A uniform heavy rod of weight 10 , N,cross-se | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The elongation $\Delta \ell$ of a rod of length $L$,cross-sectional area $A$,and Young's modulus $Y$ due to its own weight $W$ is given by the for

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(D) The elongation $\Delta \ell$ of a rod of length $L$,cross-sectional area $A$,and Young's modulus $Y$ due to its own weight $W$ is given by the formula:$\Delta \ell = \frac{WL}{2AY}$Given values:Weight $W = 10 \, 	ext{N}$Length $L = 20 \, 	ext{cm} = 0.2 \, 	ext{m}$Area $A = 100 \, 	ext{cm}^2 = 100 	imes 10^{-4} \, 	ext{m}^2 = 10^{-2} \, 	ext{m}^2$Young's modulus $Y = 2 	imes 10^{11} \, 	ext{N/m}^2$Substituting these values into the formula:$\Delta \ell = \frac{10 	imes 0.2}{2 	imes 10^{-2} 	imes 2 	imes 10^{11}}$$\Delta \ell = \frac{2}{4 	imes 10^9} = 0.5 	imes 10^{-9} \, 	ext{m}$$\Delta \ell = 5 	imes 10^{-10} \, 	ext{m}$Thus,the elongation is $5 	imes 10^{-10} \, 	ext{m}$. The value in $	imes 10^{-10} \, 	ext{m}$ is $5$.

Similar Questions

When the load applied to a wire is increased from $5 \ kg$ wt to $8 \ kg$ wt,the elongation of the wire increases from $1 \ mm$ to $1.8 \ mm$. The work done during the elongation of the wire is (Acceleration due to gravity $= 10 \ m/s^2$)

An elastic material of Young's modulus $Y$ is subjected to a stress $S$. The elastic energy stored per unit volume of the material is

$A$ wire is suspended by one end. At the other end,a weight equivalent to $20 \ N$ force is applied. If the increase in length is $1.0 \ mm$,the increase in energy of the wire will be ....... $J$.

What is the work done in stretching a uniform metal wire of length $2 \ m$ to $2.004 \ m$ with an area of cross-section $10^{-6} \ m^2$ (in $J$)? [Young's modulus of the wire = $2 \times 10^{11} \ N/m^2$]

$A$ uniform rod of length $L$ has a mass per unit length $\lambda$ and area of cross-section $A$. If the Young's modulus of the rod is $Y$,then the elongation in the rod due to its own weight is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module