Question

A system consists of two identical cubes each of mass m linked together by a massless spring of spring constant k. The spring is compressed by x connecting cubes by thread. Find minimum value of x for which lower cube will bounce up after the thread has been burnt.

• A. $\frac{2mg}{k}$
• B. $\frac{3mg}{k}$
• C. $\frac{3mg}{2k}$
• D. $\frac{mg}{2k}$

Answer 1

The correct option is B $\frac{3mg}{k}$

The elongation produced $x^{\prime }$ be such that $k{x}^{\prime }=mg$. Apply energy conservation as the maximum elongation $u_{block}=0$

$\frac{1}{2}k{x}^2=mg(x+x^{\prime })+\frac{1}{2}k{x}^{\prime 2}$

$x^2-\frac{2mgx}{k}-2\frac{mg}{k}{x}^{\prime }-x^{\prime 2}$

or $x^2-\frac{2mg}{k}x-\frac{2mg}{k}\left(\frac{mg}{k}\right)-{\left(\frac{mg}{k}\right)}^2=0$

or $x=\frac{3mg}{k}$