A loop of light inextensible string passes ov | vedclass

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

Question

(A) Let the horizontal distance between $A$ and $B$ be $2l$. Let the vertical distance of $C$ below the line $AB$ be $y$. The length of the string seg

Vedclass · Accepted Answer

$\frac{m}{M} > 2\sqrt {\frac{{\eta + 1}}{{\eta + 3}}} - 1$

Vedclass · Answer

(A) Let the horizontal distance between $A$ and $B$ be $2l$. Let the vertical distance of $C$ below the line $AB$ be $y$. The length of the string segment $AC$ is $\eta l$. By Pythagoras theorem,the horizontal distance of $C$ from the midpoint $O$ is $x = \sqrt{(\eta l)^2 - y^2}$.For the masses to cross,the mass $m$ must be able to move downwards past the level of $C$. The system is in equilibrium when the tension $T$ in the string balances the weights. At point $C$,$2T \cos 	heta = Mg$,where $\cos 	heta = y/(\eta l)$. Thus $T = Mg \eta l / (2y)$.At point $O$,the mass $m$ is supported by the tension in the vertical string. For $m$ to move down,its weight $mg$ must be greater than the upward force exerted by the string at $O$. As $m$ moves down,the angle $	heta$ changes. The condition for $m$ to reach $C$ is derived from the potential energy or force balance at the limit where $y 	o 0$. The correct condition is $\frac{m}{M} > 2\sqrt{\frac{\eta+1}{\eta+3}} - 1$.

$A$ loop of light inextensible string passes over smooth small pulleys $A$ and $B$. Two masses $m$ and $M$ are attached to the points $O$ and $C$ respectively. The condition that $m$ and $M$ will cross each other (given $AB = 2l$ and $AC = BC = \eta l$) is:

Similar Questions

$A$ light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (where $m_2 > m_1$). If the acceleration of the system is $\frac{g}{\sqrt{2}}$,then the ratio of the masses $\frac{m_1}{m_2}$ is:

In the figure shown,both blocks are released from rest. Find the time taken for them to cross each other. (Assume $g = 10 \ m/s^2$)

The tension in the string connected between the two blocks is ......... $N$.

$A$ lift of mass $1000\,kg$ is moving with an acceleration of $1\,m/s^2$ in the upward direction. The tension developed in the cable connected to the lift is ........... $N$ $(g = 9.8\,m/s^2)$.

$A$ light string passes over a frictionless pulley. To one of its ends a mass of $6\, kg$ is attached. To its other end a mass of $10\, kg$ is attached. The tension in the thread will be ........ $N$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module