A steel wire 1.5,m long and of radius 1,mm is | vedclass

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

Question

(A) At the lowest position,the tension $T$ in the wire is given by the sum of the gravitational force and the centripetal force: $T = Mg + M\omega^2\e

Vedclass · Accepted Answer

$1.77 	imes 10^{-3}\,m$

Vedclass · Answer

(A) At the lowest position,the tension $T$ in the wire is given by the sum of the gravitational force and the centripetal force: $T = Mg + M\omega^2\ell$.Here,$M = 3\,kg$,$\ell = 1.5\,m$,$g = 10\,m/s^2$,and frequency $f = 2\,Hz$.The angular velocity is $\omega = 2\pi f = 2 	imes 3.14 	imes 2 = 12.56\,rad/s$.The tension $T = 3 	imes 10 + 3 	imes (12.56)^2 	imes 1.5 = 30 + 3 	imes 157.75 	imes 1.5 = 30 + 710 = 740\,N$.The elongation $\Delta\ell$ is given by $\Delta\ell = \frac{T\ell}{AY}$,where $A = \pi r^2 = 3.14 	imes (10^{-3})^2 = 3.14 	imes 10^{-6}\,m^2$.$\Delta\ell = \frac{740 	imes 1.5}{3.14 	imes 10^{-6} 	imes 2 	imes 10^{11}} = \frac{1110}{6.28 	imes 10^5} \approx 1.77 	imes 10^{-3}\,m$.

Similar Questions

$A$ thin $1 \, m$ long rod has a radius of $5 \, mm$. $A$ force of $50 \, \pi \, kN$ is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is $0.01 \, mm$,which of the following statements is false?

The mass and length of a wire are $M$ and $L$ respectively. The density of the material of the wire is $d$. On applying a force $F$ on the wire,the increase in length is $l$. Then,the Young's modulus of the material of the wire will be:

The following four wires are made of the same material. Which one will have the largest elongation when subjected to the same tension?

$A$ rigid bar of mass $15\; kg$ is supported symmetrically by three wires each $2.0\; m$ long. Those at each end are of copper and the middle one is of iron. Determine the ratio of their diameters if each is to have the same tension.

Vedclass Test Series

Exam Paper Generator

Online Exam Module