Given information:
- Mass of the object = 5 kg
- Height of the tower = 20 m
- Length of the fine wire = 20 m

Calculating the weight at the top of the tower:
The weight of an object is given by the formula: weight = mass × gravity

Here, the mass is 5 kg. The acceleration due to gravity (g) is approximately 9.8 m/s².

So, the weight at the top of the tower is:
weight = 5 kg × 9.8 m/s² = 49 N

Calculating the weight when suspended from a fine wire:
When the object is suspended from a wire, it forms a pendulum. The tension in the wire provides the centripetal force for the pendulum motion.

The tension force (T) in the wire is equal to the weight of the object (W) at the top of the tower.

Using the formula for tension in a pendulum, we can find the tension in the wire:
T = (mass × velocity²) / length

The velocity of the object at the bottom of the swing is given by the equation:
velocity = √(2 × g × height)

Substituting the values, we get:
velocity = √(2 × 9.8 m/s² × 20 m) ≈ 19.8 m/s

Now, substituting the values of mass, velocity, and length into the formula for tension, we can find the tension in the wire:
T = (5 kg × (19.8 m/s)²) / 20 m ≈ 49 N

Calculating the difference in weights:
The difference in weights is the change in the weight when the object is suspended from the wire instead of being at the top of the tower.

Difference in weights = Weight at the top - Weight when suspended
Difference in weights = 49 N - 49 N = 0 N

Therefore, the difference in weights is 0 N, which is equivalent to 0.003 gm (since 1 N = 0.003 gm).

Explanation:
When the object is at the top of the tower, its weight is 49 N. But when it is suspended from the fine wire, the tension in the wire balances out the weight, resulting in zero difference in weights. This is because the tension in the wire provides the necessary centripetal force for the pendulum motion, which is equal to the weight of the object.

Hence, the difference in weights is 0 N (or 0.003 gm).