If a block is suspended from a string does the gravitational force do any work on it?

work done by any force is the dot product of the force vector acting on the object and displacement vector of the object. hence work done is given as

W = F. d

where F = force vector, d = displacement vector

when the block is suspended from a string at rest, there is tension force on the block in upward direction and gravitational force by earth in down direction.

since the block is not moving and is at rest, hence displacement of the block is zero.

so the work done by the gravitational force is zero as work done is product of displacement and force