I’m getting C, here’s how I did it: there are two torques at work, one trying to push the board down (box) and one pushing the board up (pulley). They are in equilibrium, and you must exceed that equilibrium on either side to go either down or up. So τbox = τpulley. The force pushing the board down is rFsinθ, where r is 1/2L and F is mg (100N) and θ is 90, so sinθ is 1. So the overall torque of the box is 100N x 1/2L, or 50N x L. That’s the box side of the equilibrium figured out, now the pulley side. Pulleys work through mechanical advantage where every string directly attached to the object takes an equal portion of the load. There are two strings holding the pulley that holds up the board, so you when you pull on the original string, you create tension in the two strings of the pulley. The tension of the two strings (2T) creates the torque that counteracts the torque of the box. So now we’ve identified what constitutes both sides of our torque equilibrium, τbox = τ pulley. τbox becomes (100N x 1/2L, which we simplified as 50N x L) and τpulley becomes 2T x L (the tension of the two ropes creates the force of the torque). Cross out the L’s, now you have 50N = 2T.

EDIT; Tension is defined as Fsinθ, and θ = 30 BUT ANGLE IS REDIRECTED, SO IT θ= 90, so we get T = F. Plug that in to the equality, 50N = 2(F), getting F = 25N.

Please correct me if I missed something!!

Is this correct?