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 an

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

$A$ wire of length $40 \text{ cm}$ is stretched by $0.1 \text{ cm}$. The strain on the wire is

The reason for the change in shape of a regular body is

$A$ force of $10 \,N$ is required to break a wire of radius $1 \,mm$. The force required to break the wire of the same material, but radius $3 \,mm$ will be

Write copper,steel,glass,and rubber in the order of increasing coefficient of elasticity.

The cross-sectional areas of steel and brass wires are $0.1 \,cm^2$ and $0.2 \,cm^2$ respectively. If the same stress is produced in both by a weight $W$,what is the ratio of the tensions $T_1/T_2$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module