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