A) ii) Calculate the weight of the body on the planet. b) Explain this observation. c) A man of mass 80 kg is standing in a lift. What force does he exert on the floor when the lift is at rest?

Mass of the body $m = 50 \, \text{g} = 0.050 \, \text{kg}$.
Acceleration of gravity on the planet $g = 1.66007 \, \text{m/s}^2$ (calculated in part i)).
The formula for weight is $W = mg$.

Rounding to two significant figures:

The weight of the body on the planet is $\boxed{\text{0.083 N}}$.

Mass $m = 80 \, \text{kg}$.
Acceleration $a = 0 \, \text{m/s}^2$ (at rest).
Acceleration due to gravity $g = 9.8 \, \text{m/s}^2$.

Since the lift is at rest, the net force is zero. The normal force $N$ balances the man's weight $mg$.

The force exerted on the floor is $\boxed{\text{784 N}}$.

Mass $m = 80 \, \text{kg}$.
Acceleration $a = 4 \, \text{m/s}^2$ (upwards).
Acceleration due to gravity $g = 9.8 \, \text{m/s}^2$.

When accelerating upwards, the net force is upwards.

The force exerted on the floor is $\boxed{\text{1104 N}}$.

Mass $m = 80 \, \text{kg}$.
Acceleration $a = 3 \, \text{m/s}^2$ (downwards).
Acceleration due to gravity $g = 9.8 \, \text{m/s}^2$.

When accelerating downwards, the net force is downwards.

The force exerted on the floor is $\boxed{\text{544 N}}$.