A thick rope of density ρ and length L is hung from a rigid support. Young's modulus of materia

English

Gujarati

Hindi

8.Mechanical Properties of Solids

easy

A thick rope of density $\rho$ and length $L$ is hung from a rigid support. The Young's modulus of the material of rope is $Y$. The increase in length of the rope due to its own weight is

A

$(1 / 4) \rho gL ^2 / Y$

B

$(1 / 2) \rho g L ^2 / Y$

C

$\rho g L ^2 / Y$

D

$\rho g L / Y$

Solution

(b)

$\Delta \ell=\frac{ F ( L / 2)}{ AY }=\frac{( AL \rho g )( L / 2)}{ AY }$

$=\left(\frac{1}{2}\right) \rho g L ^2 / Y$

Standard 11

Physics

Share

Similar Questions

On increasing the length by $0.5\, mm$ in a steel wire of length $2\, m$ and area of cross-section $2\,m{m^2}$, the force required is $[Y$ for steel$ = 2.2 \times {10^{11}}\,N/{m^2}]$

medium

A boy’s catapult is made of rubber cord which is $42\, cm$ long, with $6\, mm$ diameter of cross -section and of negligible mass. The boy keeps a stone weighing $0.02\, kg$ on it and stretches the cord by $20\, cm$ by applying a constant force. When released, the stone flies off with a velocity of $20\, ms^{-1}$. Neglect the change in the area of cross section of the cord while stretched. The Young’s modulus of rubber is closest to

medium

(JEE MAIN-2019)

A rod of uniform cross-sectional area $A$ and length $L$ has a weight $W$. It is suspended vertically from a fixed support. If Young's modulus for rod is $Y$, then elongation produced in rod is ……

easy

What is Young’s modulus ? Explain. and Give its unit and dimensional formula.

medium

Longitudinal stress of $1\,kg/m{m^2}$ is applied on a wire. The percentage increase in length is $(Y = {10^{11}}\,N/{m^2})$

medium