Two blocks having masses `8kg` and `16kg` are connected to the two ends of a light spring. The system is placed on a smooth horizontal floor. An inextensible string also connects B with ceiling as shown in the figure at the initial moment. Initially the spring has its natural length. A constant horizontal force F is applied to the heavier block as shown. What is the maximum possible value of F so the lighter block doesn't loose contact with ground?

Answer

`30N`

Explanation

Draw FBD of B to get extension in spring. Instant when block B just loses contact with ground net force on it is zero.
`kx-Tcos theta=0impliesTsintheta+N-mg=0` to rise `N=0`
`(kx)/(costheta)sintheta=mg`
`x=(mg)/(ktantheta)=(80)/(kxx(4//3))=60/k`
If spring has to just extend till this value at their extension it should be at rest.
Now we apply work energy theorem to get
`F_x=1/2kx^2impliesF=30N`