Question

derive an expression for potential energy when an object of mass m is taken to height h

Answer 1

a) An object increases its energy when raised through a height. This is because work is done on it against gravity while it is being raised. The energy present in such an object is the gravitational-potential energy. This gravitational-potential energy of an object at a point above the ground is defined as the work done in raising it from the ground to that point against gravity.
An object of mass m, when raised through a height h from the ground, then work done by this object will be
W = force x displacement = mg x h = mgh

(b) Potential energy will be the work done by the object i.e.,
W = mgh = 10 x 9.8 x 6 = 588 J

Answer 2

here the object with mass m is raised to a height h