Gravitational potential difference between surface of a planet and a point situated at a height of 20 m above its surface is 2 joule/kg. If gravitational field is uniform, then the work done in taking a 5 kg body of height 4 meter above surface will be:

• A: 2 J
• B: 20 J
• C: 40 J
• D: 10 J

To find the work done in lifting a 5 kg body to a height of 4 meters above the surface of the planet, we can use the concept of gravitational potential energy. The gravitational potential difference given is 2 joules per kilogram, which means that for every kilogram, the potential energy increases by 2 joules for every meter of height.

Calculating Work Done

The formula for work done (W) when lifting an object in a uniform gravitational field is:

W = m × g × h

• m = mass of the object (5 kg)
• g = gravitational potential difference (2 J/kg)
• h = height (4 m)

Substituting the Values

Now, substituting the values into the formula:

W = 5 kg × 2 J/kg × 4 m

This simplifies to:

W = 5 × 2 × 4 = 40 J

Final Answer

The work done in taking the 5 kg body to a height of 4 meters is 40 joules. Therefore, the correct option is C: 40 J.