When a load of 80 ,N is suspended from a stri | vedclass

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

Question

(D) According to Hooke's Law,the extension $\Delta l$ is proportional to the applied force $T$. Let $l_0$ be the natural length and $k$ be the force c

Vedclass · Accepted Answer

$10.5$

Vedclass · Answer

(D) According to Hooke's Law,the extension $\Delta l$ is proportional to the applied force $T$. Let $l_0$ be the natural length and $k$ be the force constant of the string.The length $l$ under tension $T$ is given by $l = l_0 + \frac{T}{k}$.For $T_1 = 80 \,N$,$l_1 = 101 \,mm = l_0 + \frac{80}{k}$  --- $(1)$For $T_2 = 100 \,N$,$l_2 = 102 \,mm = l_0 + \frac{100}{k}$ --- $(2)$Subtracting $(1)$ from $(2)$: $102 - 101 = \frac{100-80}{k} \implies 1 = \frac{20}{k} \implies k = 20 \,N/mm$.Substituting $k$ into $(1)$: $101 = l_0 + \frac{80}{20} \implies 101 = l_0 + 4 \implies l_0 = 97 \,mm$.Now,for $T_3 = 160 \,N$,the length $l_3 = l_0 + \frac{T_3}{k} = 97 + \frac{160}{20} = 97 + 8 = 105 \,mm$.Converting to cm: $105 \,mm = 10.5 \,cm$.

Column-$I$	Column-$II$
$(a)$ $\text{Stress} \propto \text{Strain}$	$(i)$ $M^1 L^{-1} T^{-2}$
$(b)$ $\text{Dimensional formula for compressibility}$	$(ii)$ $M^{-1} L^1 T^2$
	$(iii)$ $\text{Poisson's ratio}$
	$(iv)$ $\text{Hooke's law}$

When a load of $80 \,N$ is suspended from a string,its length is $101 \,mm$. If a load of $100 \,N$ is suspended,its length is $102 \,mm$. If a load of $160 \,N$ is suspended from it,then the length of the string is (Assume the area of cross-section is unchanged). (in $\,cm$)

Similar Questions

Two equal and opposite forces each $F$ act on a rod of uniform cross-sectional area $a$ as shown in the figure. The shearing stress on the section $AB$ 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 $\text{ mm}$)

The length of a rod under longitudinal tension $T_1$ is $L_1$ and that under longitudinal tension $T_2$ is $L_2$. What is the actual length of the rod,in the absence of tensions?

Two wires $A$ and $B$ are stretched by the same load. If the area of cross-section of wire $A$ is double that of wire $B$,then the stress on wire $B$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module