force n friction

(a)
take FBD of mass in right...
The forces are.. P to right... and friction towards left and tension towards left... And as P<F₀ so, friction = P hence T=0

(b)
If F₀<P<2F₀ then again FBD of right mass..
the forces are P to right... F₀ to left and T to left... and as P<2F₀ so system is in equilibrium...
Hence P=T+F₀ == > T=P-F₀

(c)
P>2F₀ ==> net acceleration is (P-2F₀)/2m
Take FBD of right mass...
P to right, T and F₀ to left
So, P-T-F₀ = m.(P-2F₀)/2m
==> P-T-F₀ = P/2 - F₀
==> T = P/2

so ans is (a),(b),(c)

tx :)