Question

Block 'A' is hanging from a vertical spring and is at rest block 'B' strikes the block 'A' with velocity 'v' and strikes to it. And v is such that it just attends natural length, then choose the correct option(s):

• A. $v=\sqrt{\frac{6m{g}^2}{k}}$
• B. $v=\sqrt{\frac{10m{g}^2}{k}}$
• C. $v=\sqrt{\frac{9m{g}^2}{k}}$
• D. None of these

Answer 1

The correct option is A $v=\sqrt{\frac{6m{g}^2}{k}}$

assuming masses same,

$0.5m{v}^2=0.5\left(m+m\right)v^2+0.5k{x}^2----\left(1\right)$

and.

to gain natural length again,

$mgx=0.5\left(m+m\right)v^2----\left(2\right)$

On solving both equation we get

$v=\sqrt{\frac{6m{g}^2}{k}}$

Hence, option $A$ is the correct answer.