Question

A flexible chain of length L = 20$\surd 2$ m and mass W = 10 kg is initially placed at rest on a smooth frictionless wedge surface ABC. It is given a slight jerk on one side so that it will start sliding on the side. Find the speed of the chain when its one end will leave the vertex of the wedge

• A. $10\surd 2m/s$
• B. $10m/s$
• C. $4m/s$
• D. $(10\surd 2{)}^{1/2}m/s$

Answer 1

The correct option is B $10m/s$

A flexible chain of length $L=20\sqrt{2}m$ and mass $m=10kg$ placed at rest on the smooth,

From the first figure, initially

The center of mass is at Point $M$

$sin45=\frac{BM}{5\sqrt{2}}$

$BM=5m$

When it is given a slight jerk on one side on that it will start sliding on one side.

From the 2nd figure

The center of mass is at point $D$,

$Sin45=\frac{BP}{10\sqrt{2}}$

$BP=10m$

so, we can say that the center of mass descended to $10m$ from the $5m$ from the reference.

By the conservation of energy,

the gain in kinetic energy is equal to the loss in potential energy

$\Delta U=\Delta K$

$-mg\left(5\right)-(-mg10)=\frac{1}{2}m{v}^2$

$5mg+10mg=\frac{1}{2}m{v}^2$

$5mg=\frac{1}{2}m{v}^2$

$v^2=10g$

$v=10m/s$,

The velocity of chain is $10m/s$

Thus, the correct option is B.