Explanation

(d) Centre of mass of a stick lies at the mid point and when the stick is displaced through an angle $60{^\circ}$ it rises upto height $'h'$ from the initial position
From the figure $h = \frac{l}{2} - \frac{l}{2}\cos{\theta = \frac{l}{2}(1 - \cos\theta)}$
Hence the increment in potential energy of the stick $= mgh = mg\frac{l}{2}\left( 1 - \cos\theta \right) = 0.4 \times 10 \times \frac{1}{2}\left( 1 - \cos{60{^\circ}} \right) = 1J$