Consider the situation shown in the figure. T | vedclass

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

Question

(C) Let the acceleration of the system be $a$. The equation of motion for the system is:$T - F = m_1a$ (for mass $m_1$)$m_2g - T = m_2a$ (for mass $m_

Vedclass · Accepted Answer

$\frac{m_2g(2m_1 + m_2)}{2AY(m_1 + m_2)}$

Vedclass · Answer

(C) Let the acceleration of the system be $a$. The equation of motion for the system is:$T - F = m_1a$ (for mass $m_1$)$m_2g - T = m_2a$ (for mass $m_2$)Adding these equations: $m_2g - F = (m_1 + m_2)a$Given $F = m_2g/2$,we have $m_2g - m_2g/2 = (m_1 + m_2)a$,so $a = \frac{m_2g}{2(m_1 + m_2)}$.Now,find the tension $T$ in the string using the equation for $m_2$:$T = m_2(g - a) = m_2(g - \frac{m_2g}{2(m_1 + m_2)}) = m_2g(1 - \frac{m_2}{2(m_1 + m_2)}) = m_2g(\frac{2m_1 + 2m_2 - m_2}{2(m_1 + m_2)}) = \frac{m_2g(2m_1 + m_2)}{2(m_1 + m_2)}$.The strain is given by $	ext{Strain} = \frac{	ext{Stress}}{Y} = \frac{T}{AY}$.Substituting $T$: $	ext{Strain} = \frac{m_2g(2m_1 + m_2)}{2AY(m_1 + m_2)}$.Thus,the correct option is $C$.

Consider the situation shown in the figure. The force $F$ is equal to $m_2g/2$. If the area of cross-section of the string is $A$ and its Young's modulus is $Y$,find the strain developed in it. The string is light and there is no friction anywhere.

Similar Questions

Two wires $A$ and $B$ of the same length are made of the same material. The load $(F)$ vs. elongation $(x)$ graph for these two wires is shown in the figure. Which of the following statement$(s)$ is/are true?

If $\delta$ is the depression produced in a beam of length $L$,breadth $b$ and thickness $d$,when a load $W$ is placed at the mid-point,then:

$A$ steel wire of length $4.7\; m$ and cross-sectional area $3.0 \times 10^{-5}\; m^{2}$ stretches by the same amount as a copper wire of length $3.5\; m$ and cross-sectional area of $4.0 \times 10^{-5}\; m^{2}$ under a given load. What is the ratio of the Young's modulus of steel to that of copper?

$A$ ring of a thin wire of cross-sectional area $a$ and length $l$ is dipped into a liquid of surface tension $\sigma$ and taken out so that a film of liquid is formed in the ring. If Young's modulus of the material of the wire is $Y$,then the longitudinal strain developed in the ring will be:

Young's modulus of elasticity of a material depends upon

Vedclass Test Series

Exam Paper Generator

Online Exam Module