A body of mass 20 kg is at a height of 8 m above the ground. Taking g = 9.8 m/s^2, what is the gravitational potential energy possessed by the body relative to the ground?

Introduction / Context:
Gravitational potential energy is the energy stored in a body due to its position in a gravitational field. Near the Earth surface, this energy is directly proportional to the mass of the body, the height above a reference level, and the acceleration due to gravity. This question asks you to apply the basic formula for gravitational potential energy to a specific set of values for mass, height, and g.

Given Data / Assumptions:

• Mass of the body, m = 20 kg.
• Height above the ground, h = 8 m.
• Acceleration due to gravity, g = 9.8 m/s^2.
• The reference level for potential energy is the ground, where potential energy is taken as zero.
• We use the formula for gravitational potential energy near Earth surface.

Concept / Approach:
The gravitational potential energy U of a body of mass m at height h above a reference level in a uniform gravitational field is given by the formula U = m * g * h. Here m is in kilograms, g in m/s^2, and h in metres. The resulting potential energy is measured in joules (J), where 1 J = 1 kg * m^2 / s^2. Once we substitute the given values into this formula, we can compute the numeric value and identify the correct unit among the options.

Step-by-Step Solution:
Step 1: Write the formula for gravitational potential energy: U = m * g * h. Step 2: Substitute the given values: m = 20 kg, g = 9.8 m/s^2, and h = 8 m. Step 3: Compute the product g * h: 9.8 * 8 = 78.4. Step 4: Multiply by the mass: U = 20 * 78.4 = 1568. Step 5: Attach the correct unit. Since we used kg, m, and m/s^2, the unit is kg * m^2 / s^2, which is called the joule (J). So U = 1568 J.

Verification / Alternative check:
Check the order of magnitude. A 10 kg mass at 10 m height with g taken as roughly 10 m/s^2 would have U approximately 10 * 10 * 10 = 1000 J. In this problem, the mass is 20 kg and height is 8 m with g slightly less than 10, which should give a value somewhat above 1500 J. The computed value 1568 J fits this expectation. Also, asking whether coulomb, watt, or newton could be the unit of energy immediately confirms that joule is appropriate for potential energy in mechanics.

Why Other Options Are Wrong:
1568 C: Coulomb (C) is the unit of electric charge, not mechanical energy. 1568 W: Watt (W) is the unit of power, which is energy per unit time, not energy itself. 1568 N: Newton (N) is the unit of force, equal to kg * m / s^2, not kg * m^2 / s^2.

Common Pitfalls:
Students sometimes forget to include the height or the acceleration due to gravity in the formula, or they choose the wrong unit at the end. Mixing up joule, watt, and newton is especially common, because all three appear in mechanics problems. To avoid this, remember that energy and work are always in joules, power is in watts, and force is in newtons. Also be careful with g; using 10 m/s^2 as an approximation is acceptable for rapid calculations, but here the value 9.8 m/s^2 leads to the more precise result 1568 J.

Final Answer:
The gravitational potential energy of the 20 kg mass at a height of 8 m is 1568 J.