The length of an elastic string is a metres w | vedclass

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

Question

(B) According to Hooke's Law, the extension of an elastic string is proportional to the applied tension. Let $l$ be the natural length of the string a

Vedclass · Accepted Answer

$5b-4a$

Vedclass · Answer

(B) According to Hooke's Law, the extension of an elastic string is proportional to the applied tension. Let $l$ be the natural length of the string and $k$ be the force constant.The length of the string under tension $T$ is given by $L = l + \frac{T}{k}$.For $T_1 = 4 \ N$, $L_1 = a = l + \frac{4}{k} \implies \frac{4}{k} = a - l$  (Equation $1$).For $T_2 = 5 \ N$, $L_2 = b = l + \frac{5}{k} \implies \frac{5}{k} = b - l$  (Equation $2$).Subtracting Equation $1$ from Equation $2$: $\frac{5}{k} - \frac{4}{k} = (b - l) - (a - l) \implies \frac{1}{k} = b - a$.Substituting $\frac{1}{k}$ into Equation $1$: $a = l + 4(b - a) \implies a = l + 4b - 4a \implies l = 5a - 4b$.Now, for $T_3 = 9 \ N$, the length $x$ is $x = l + \frac{9}{k}$.Substituting $l = 5a - 4b$ and $\frac{1}{k} = b - a$:$x = (5a - 4b) + 9(b - a) = 5a - 4b + 9b - 9a = 5b - 4a$.

The length of an elastic string is $a$ metres when the longitudinal tension is $4 \ N$ and $b$ metres when the longitudinal tension is $5 \ N$. The length of the string in metres when the longitudinal tension is $9 \ N$ is

Similar Questions

Stress to strain ratio is equivalent to

What is stress? Give its two definitions.

Which one of the following quantities does not have the unit of force per unit area?

The breaking stress for a wire of radius $r$ of a given material is $F \ Nm^{-2}$. The breaking stress for a wire of the same material of radius $2r$ will be:

The elastic limit of a metal is $\frac{400}{\pi} \text{ MPa}$. If a rod of this metal is to support a $484 \text{ N}$ load without exceeding its elastic limit, the minimum diameter of the rod is: (in $\text{ mm}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module