A

(i) The work done by gravity is:
The gravitational force acting on the block is $F_g = Mg$, where $g$ is the acceleration due to gravity. Since the platform is accelerating upwards with an acceleration $a$, the effective acceleration acting on the block is $g - a$.
The distance moved by the block in time $T$, under upward acceleration is given by the equation of motion:
$$ d = rac{1}{2}(g - a)T^2 $$
Therefore, the work done by gravity is:
$$ W_g = -F_g imes d = -Mg imes rac{1}{2}(g - a)T^2 = -rac{1}{2}Mg(g - a)T^2 $$
(ii) The work done by the normal reaction is:
The normal force $N$ exerted on the block must balance the weight of the block and provide the upward acceleration:
$$ N = M(g + a) $$
The work done by the normal reaction is given by:
$$ W_N = N imes d = M(g + a) imes rac{1}{2}(g - a)T^2 = rac{1}{2}M(g + a)(g - a)T^2 $$
(iii) The change in kinetic energy of the block is:
The change in kinetic energy $ riangle KE$ is equal to the work done by all forces acting on the block:
$$ riangle KE = W_N + W_g = rac{1}{2}M(g + a)(g - a)T^2 - rac{1}{2}Mg(g - a)T^2 $$
After simplification, using the work-energy principle, we can find the change in kinetic energy concerning the given parameters.