Three balls of mass 10 kg, 20 kg and 10 kg are hanging by a massless string and are connected by massless springs as shown in the figure below. Initially the system is in equilibrium and all the objects are at rest.
If the string at the top snaps suddenly, what is the acceleration of the topmost ball at that instant of time? [In the following, g denotes the acceleration due to gravity]
(a) $0\quad$ (b) $2g\quad$ (c) $g\quad$ (d) $4g\quad$ (e) $3g$
My conceptual understanding is rather not good although I can give couple of attempts.
Answer: $g$, since the only external force acting is gravity. But I think the spring attached to two masses might exert force.
taking the bottom mass, $10g = -k(x_2-x_1)$
the mass in the middle, $20g = -kx_1+k(x_2-x_1)$
adding both gives me $30g = -kx_1$
at the topmost ball,
$$T-10g-30g = -10g\\ T=0\quad g=4g$$ [$T$ tension in the string, $x_1$ displacement of the spring between topmost mass and mass in the middle, $x_2$ displacement of the spring between mass in the middle and bottom most]
Please clarify the concept that I might be mixing up and give the solution if my attempts are not correct.