Answer:
(a) 
(b) 
Explanation:
Given:
- Limiting tension of snapping of the rope, T= 387 N
- Weight of the object to be lifted,

- ∴mass,

- height of letting down the weight, h = 6.1 m
(a)
Now,
The force to be compensated for being on the verge of snapping:
(T-w) = 62 N
Therefore, we need to produce and acceleration equivalent to the above force.
∵



(b)
From the equation of motion ,we have:
....................(2)
where:
u= initial velocity= 0 (here, starting from rest)
v= final velocity = ?

s= displacement =h =6.1 m
Now, putting the values in eq. (2)

is the velocity with which the body will hit the ground in the given conditions.
I am pretty sure the correct answer is C.
The amount of energy is ALWAYS conserved based on the law of conservation of energy. Therefore, the amount of energy will remain the same.