Rotational motion question, can anyone check over this result please?

[knowlewj01]

Homework Statement

An inextensible light string of length 2 m is fixed at one end A and carries at its other end B a particle of mass 3 kg, which is rotating in a horizontal circle whose centre is 1 m vertically below A. Find the angular velocity of the particle and the tension in the string.

Homework Equations

Attached my diagram with my solution.

The Attempt at a Solution

could someone take a look at this to make sure i have gone about it correctly. thanks.

 

[kuruman]

Looks good.