Tension connecting two collinear rotating objects

[songoku]

Homework Statement

Two objects of mass 3 kg and 4 kg are rotating in vertical circle. Mass 3 kg is connected to the center of rotation by string 1 and mass 3 kg and 4 kg are connected by string 2. The length of each string is 0.5 m and the two objects are always collinear when rotating. If the tangential speed of 3 kg object is 4 m/s, find the magnitude of tension in string 2 when they are at the top of the trajectory

Relevant Equations

$v=\omega .r$

$F=m.a$

$a=\frac{v^2}{r}$

Tangential speed of 4 kg object is 8 m/s

At the top of the trajectory, there will be two downwards forces acting on 4 kg object, which are tension of string 2 (T₂) and weight

$F=m.a$
$W + T_2=m.\frac{v^2}{r}$

Putting all the values, I get negative value for T₂. Where is my mistake?

Thanks

 

[haruspex]

I get negative value for T2

Strange... I don't. Please fill in the details.

 

[songoku]

Strange... I don't. Please fill in the details.

Never mind. I have checked several times before posting and didn't spot the mistake but only from once reading what you wrote I directly see my mistake. My dumbness just has no limit.

Thank you very much haruspex and happy new year