A uniform metal chain of mass m and length 'L' passes over a massless and frictionless pulley. It is released from rest with a part of its length ' l ' is hanging on one side and rest of its length ' L -l ' is hanging on the other side of the pulley. At a certain point of time, when l=( L / x ), the acceleration of the chain is ( g /2). The value of x is ldots ldots . ..

Question

A uniform metal chain of mass m and length 'L' passes over a massless and frictionless pulley. It is released from rest with a part of its length ' l ' is hanging on one side and rest of its length ' L -l ' is hanging on the other side of the pulley. At a certain point of time, when l=( L / x ), the acceleration of the chain is ( g /2). The value of x is ldots ldots . .. (A) 6 (B) 2 (C) 1.5 (D) 4

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/73d00c25bed9e8204ccbc4df9650309a-.png" /> a =(( m 2- m 1)/( m 2+ m 1)) g ( g /2)=((λ( L -ℓ)-λ ℓ) g /λ L ) ⇒ L =( L /4)=( L / x ) x =4

6

2

1.5

4

a=(m2​+m1​)(m2​−m1​)​g 2g​=λL(λ(L−ℓ)−λℓ)g​ ⇒L=4L​=xL​ x=4

$a = \frac{( m _{2} - m _{1} )}{( m _{2} + m _{1} )} g$
$\frac{g}{2} = \frac{( λ ( L - ℓ ) - λ ℓ ) g}{λ L}$
$\Rightarrow L = \frac{L}{4} = \frac{L}{x}$
$x = 4$