Question

A uniform chain of length 2L. is hanging in equilibrium position.If end B is given a slightly downward displacement the imbalance causes an acceleration.Here pulley is small and smooth & string is inextensible. The acceleration of end B when it has been displaced by distance x , is

• A. $\frac{x}{L}g$
• B. $\frac{2x}{L}g$
• C. $\frac{x}{2L}g$
• D. g

Answer 1

The correct option is A $\frac{x}{L}g$

$\begin{array}{c}\text{when , B will}\\ \text{displaced by}x\\ \text{length of}AC\text{string}L-x\\ \text{and length of}Bc\text{string}L+x\\ \text{unit}\mathrm{mass}=\frac{m}{L}\\ \therefore \text{for mass of 'AC' string}\end{array}$

$\frac{m}{L}(L-x)a=T-\frac{m}{L}(L-x)g$

$\text{for}\text{mass of}B{C}^{\prime }\text{string}$

$\frac{m}{L}(L+x)a=\frac{m}{L}(L+x)g-T$

$\frac{m}{L}a(L-x+L-x)=\frac{m}{2}g(L+x+L+x)$

$2\cdot a=g\cdot x$

$a=\frac{gx}{2}$

Ans A