Question

Two blocks are connected by a spring, the combination is suspended at rest, from a string attached to the ceiling, as shown in the figure, the string breaks suddenly. Immediately after the string breaks, what is the initial downward acceleration of the upper block of mass 2m?

• A. $0$
• B. $\frac{3g}{2}$
• C. $g$
• D. $2g$

Answer 1

The correct option is B $\frac{3g}{2}$

The given arrangement can be reframed as shown below

From the FBD of $m$ it is clear that $kx=mg$
Just after cutting, the tension in the string will be zero. So, from the FBD of $2m$ we have
$\Rightarrow 2mg+kx-T=2ma\Rightarrow 2mg+mg-0=2ma$
$\therefore a=\frac{3mg}{2m}=\frac{3g}{2}$