Problem Analysis:
We are given the initial height of the balloon as 81m and the velocity at which it is ascending as 12m/s. We need to find the time it takes for a 2kg body dropped from the balloon to reach the surface of the earth.

Solution:

To solve this problem, we need to consider the motion of the body in two parts:
1. The motion of the balloon
2. The motion of the body

Motion of the balloon:
The balloon is ascending upwards with a velocity of 12m/s. As there is no external force acting on the balloon, its acceleration is zero. Using the equation of motion:

v = u + at

Where:
v = final velocity (12m/s)
u = initial velocity (0m/s)
a = acceleration (0m/s²)
t = time taken

We can rearrange the equation to solve for time:

t = (v - u) / a
t = (12 - 0) / 0
t = ∞

The time taken for the balloon to reach the surface of the earth is infinite as it is continuously ascending.

Motion of the body:
The body is dropped from the balloon at a height of 81m. The only force acting on the body is gravity, which causes it to accelerate downwards at a rate of 10m/s². Using the equation of motion:

s = ut + 1/2at²

Where:
s = displacement (81m)
u = initial velocity (0m/s)
a = acceleration (10m/s²)
t = time taken

We can rearrange the equation to solve for time:

81 = 0t + 1/2 * 10 * t²
81 = 5t²
t² = 81/5
t² = 16.2
t = √16.2
t ≈ 4.02s

Therefore, the body will reach the surface of the earth in approximately 4.02 seconds.

Conclusion:
In conclusion, the body dropped from the balloon will take approximately 4.02 seconds to reach the surface of the earth. The time taken for the balloon to reach the surface is infinite as it is continuously ascending.