$(a)$ Define potential energy. Write an expression for potential energy of an object of mass $m$ raised through a height $h$.
$(b)$ Find the energy possessed by an object of mass $10 \, kg$ when it is raised to a height of $6 \, m$ above the ground. (Given $g = 9.8 \, m s^{-2}$)

(N/A) Potential energy is the energy stored in an object due to its position or configuration. Gravitational potential energy of an object at a height $h$ above the ground is defined as the work done in raising it from the ground to that point against gravity.
For an object of mass $m$ raised through a height $h$, the work done $W$ is given by:
$W = \text{force} \times \text{displacement} = (m \times g) \times h = mgh$
Thus, the potential energy $PE = mgh$.
$(b)$ Given:
Mass $m = 10 \, kg$
Height $h = 6 \, m$
Acceleration due to gravity $g = 9.8 \, m s^{-2}$
Potential energy $PE = mgh = 10 \times 9.8 \times 6 = 588 \, J$.