Question

An object thrown at a certain angle to the ground.The initial and the final points of the path of the object lie on the same horizontal line.What is the work done by the force of gravity on the object?

Answer 1

When an object is thrown at a certain angle, it rises to a certain height and then comes back while moving in a parabolic path. Let h be the maximum height to which it rises.
As it rises, its kinetic energy decreases but its potential energy increases.
Potential energy gained by it in rising to the highest point = work done against gravity. 
= - mg x h = -mgh
As the body falls down, it gains kinetic energy = work done by the force due to gravity.
mg x h = mgh
Net work done by the force due to gravity
= - mgh + mgh = 0
In simple words both initial and final position lie on same horizontal line,so there is no vertical displacement i.e, height is 0.
force of gravity=MGH=m×g×0=0
So, no work is done by gravity.
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Answer 2

as in this case the object will make an angle of 90°. Thus due to cos rule it would be 0. Work done would be 0