In which of the following cases is work being done on an object? question 2 options: pulling a trailer up a hill carrying a box down a corridor suspending a heavy weight with a strong chain pushing against a locked door

Work is done when a force acts on an object AND the object moves in the direction of the force.

-- Pulling a trailer up a hill.  YES. The trailer is moving in the direction of the pulling force.  

-- Carrying a box down a corridor.  No. The box is not moving in the direction of gravity (down) OR in the direction of your arm (down the corridor).

-- Suspending a heavy weight with a strong chain,  No.  There's a force (gravity) acting on the weight, but the weight is not moving at all.

-- Pushing against a locked door.  No.  There's a force (your muscles) acting on the door, but he door is not moving at all.