A truck is pulling a car out of a ditch by me | vedclass

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

Question

(A) The formula for Young's modulus $(Y)$ is given by $Y = \frac{F \cdot l}{A \cdot \Delta l}$,where $F$ is the force,$l$ is the original length,$A$ i

Vedclass · Accepted Answer

$4.64 	imes 10^{-4} \, m$

Vedclass · Answer

(A) The formula for Young's modulus $(Y)$ is given by $Y = \frac{F \cdot l}{A \cdot \Delta l}$,where $F$ is the force,$l$ is the original length,$A$ is the cross-sectional area,and $\Delta l$ is the change in length.Rearranging for $\Delta l$,we get $\Delta l = \frac{F \cdot l}{A \cdot Y}$.The cross-sectional area $A = \pi r^2$,where $r = 5 	imes 10^{-3} \, m$.Substituting the values: $A = 3.14 	imes (5 	imes 10^{-3})^2 = 3.14 	imes 25 	imes 10^{-6} = 7.85 	imes 10^{-5} \, m^2$.Now,$\Delta l = \frac{800 	imes 9.1}{7.85 	imes 10^{-5} 	imes 2 	imes 10^{11}}$.$\Delta l = \frac{7280}{15.7 	imes 10^6} = 463.69 	imes 10^{-6} \, m = 4.6369 	imes 10^{-4} \, m$.Rounding to two decimal places,the stretch is approximately $4.64 	imes 10^{-4} \, m$.

$A$ truck is pulling a car out of a ditch by means of a steel cable that is $9.1 \, m$ long and has a radius of $5 \, mm$. When the car just begins to move,the tension in the cable is $800 \, N$. How much has the cable stretched? (Young's modulus for steel is $2 \times 10^{11} \, N/m^2$)

Similar Questions

The interatomic distance for a metal is $3 \times 10^{-10} \ m$. If the interatomic force constant is $3.6 \times 10^{-9} \ N/\mathring{A}$,then the Young's modulus in $N/m^2$ will be:

$A$ wire of length $L$ and radius $r$ is rigidly fixed at one end. On stretching the other end of the wire with a force $F$,the increase in length is $l$. If another wire of the same material but double the length and double the radius is stretched with a force $2F$,then the increase in length is:

$A$ thick brass wire of length $L$ and density $\rho$ is suspended from a rigid support. Due to its own weight,$\ell$ is the increase in length. The Young's modulus $Y$ of the brass wire in terms of density is $(g = \text{acceleration due to gravity})$

Vedclass Test Series

Exam Paper Generator

Online Exam Module