A uniform chain of length L which hangs parti | vedclass

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

Question

(C) Let $M$ be the total mass of the chain of length $L$. The mass per unit length is $\lambda = \frac{M}{L}$.When a length $l$ hangs from the table,t

Vedclass · Accepted Answer

$\frac{l}{L - l}$

Vedclass · Answer

(C) Let $M$ be the total mass of the chain of length $L$. The mass per unit length is $\lambda = \frac{M}{L}$.When a length $l$ hangs from the table,the mass of the hanging part is $m_1 = \lambda l = \frac{M}{L} l$.The mass of the part remaining on the table is $m_2 = \lambda (L - l) = \frac{M}{L} (L - l)$.For the chain to be in equilibrium,the downward force due to the hanging part must be balanced by the maximum static frictional force acting on the part on the table.The downward force is $F_g = m_1 g = \frac{M}{L} l g$.The maximum frictional force is $f_{max} = \mu N = \mu m_2 g = \mu \frac{M}{L} (L - l) g$.Equating the two: $\frac{M}{L} l g = \mu \frac{M}{L} (L - l) g$.Solving for $\mu$: $\mu = \frac{l}{L - l}$.

$A$ uniform chain of length $L$ which hangs partially from a table,is kept in equilibrium by friction. The maximum length that can hang without slipping is $l$. Then,the coefficient of friction between the table and the chain is:

Similar Questions

$A$ block of mass $m$ slides down a plane inclined at an angle $\theta$. Which of the following will $NOT$ increase the energy lost by the block due to friction?

$A$ homogeneous cubical brick lies motionless on a rough inclined surface. The half of the brick which applies greater pressure on the plane is:

$A$ uniform ladder of length $5 \ m$ is placed against a wall as shown in the figure. If the coefficient of friction $\mu$ is the same for both the wall and the floor,what is the minimum value of $\mu$ for it not to slip?

The force required to move a body up a rough inclined plane is double the force required to prevent the body from sliding down the plane. The coefficient of friction,when the angle of inclination of the plane is $60^{\circ}$ is

$A$ block of mass $4 \ kg$ is at rest on a rough inclined plane making an angle of $\theta$ with the horizontal. The coefficient of static friction between the block and the plane is $0.5$ and the frictional force on the block is $14.14 \ N$. Find the value of $\theta$. (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module