Particles connected with a string

[erisedk]

Homework Statement

Two particle of mass m each are tied at the ends of a light string of length 2a. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance ‘a’ from the center P (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force F. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes 2x is

Homework Equations

The Attempt at a Solution

http://2.bp.blogspot.com/_lRKubY9oOyI/RrGGAxqjRUI/AAAAAAAAAHQ/TtdYi47lpDc/s1600-h/Newton

2Tsinθ = F
T = F/2sinθ
where sinθ = (a² - x²)^1/2 / a
Net force on each particle is T.
So T = ma_acceleration
So, a_acceleration = F/2msinθ

However, the answer is F/2mtanθ. I don't get why. Please help?

 

[drvrm]

Net force on each particle is T.
So T = maacceleration
So, aacceleration = F/2msinθ

Draw a free body diagram of the mass- do you get the net force on it to be T? you are making some serious error-the motion is along the plane towards the other body so net force can not be T.