maths question

hi, please could i have help on part a? I thought Q will move upwards because it is lighter and P will move down the slope?
thanks!

The force on Q due to gravity is
2g
and the force on P due to gravity down the slope is
3g sin(30)
The former is larger so Q will move down and P up the slope.

ohh ok, i just considered the mass, thanks!

Sure, the whole point of the string is that you think about the ends being pulled "along" the string, with the pulley altering the direction and tension acts along the string transferring the forces. When you resolve gravity on P, the normal reaction of the plane is equal and opposite to cos(30) of the gravitational force. So that leaves sin(30) of gravity acting down the plane.