Questions on Gravitational Potential Energy

Gravitational potential energy is the form of energy that an object has or obtains because of the change in its position while in a gravitational field. Gravitational potential energy is a sort of energy that is linked with gravity or gravitational force. In this article, we will discuss the meaning of some important questions and answers and what are some important questions on gravitational potential energy. 

What is gravitational potential energy?

When the energy needed to displace a body of mass under the influence of gravity is stored in the form of potential energy when it is transferred from infinity to a location inside the gravitational potential energy. 

We all understand that the potential energy of a body can be defined as the energy stored in the body at that specific position. When external forces modify the position of the body, the change in potential energy is equal to the amount of work done on the body by the forces. The work that gravitational force does is free of the path used for an alternation in position, making it a conservative force. Furthermore, all of these forces have some potential. The gravitational force on a body at infinity is zero. Hence, potential energy is zero. So, it is taken as a reference point.

The zero of gravitational potential energy is selected freely, which is intriguing. In other words, we can choose any vertical level as the position where h = 0. A convenient zero point for simple mechanics problems might be the laboratory floor or the surface of a table. In theory, though, we might choose any reference point, also known as a datum. If the item passes below the zero point, the gravitational potential energy may even be negative. 

Some important questions on gravitational potential energy are as follows:

What is the formula for gravitational potential energy?

The formula for gravitational potential energy (U) can be iterated as follows:

U=mgh

Where the mass in kilograms is denoted by m.

The acceleration owing to gravity is denoted by the letter g. (9.8 on earth).

h is the height in metres above the ground.

What is the expression for gravitational potential energy?

If we express the gravitational potential energy, then we can define it as a body which is taken to the earth’s surface to a point at a height ‘h’ above the surface of the earth, then ri= R and rf = R + h then,

 U=GMm[1R-1(R+h)]

U=GMmhR(R+h)

When, h<R, then, 

R + h = R and g =GM/R2.

When we plug this into the equation above, we obtain

 ΔU = mgh

What is gravitational potential?

Gravitational potential is the amount of effort needed to move a unit test mass from infinity into the gravitational effects of a source mass. In simple terms, it is the gravitational potential energy inhabited by a unit mass.

V = U/m

V = -GM/r

It is important to note that, near a given position, the gravitational potential is always negative, and V is greatest at infinity. J/Kg is the SI unit for gravitational potential, and the dimensional formula is M0L2T-2.

What is gravitational self energy?

The work done by an agent in assembling a body from microscopic elements that were previously located at an infinite distance is defined as gravitational self-energy.

The gravitational self-energy of a system of ‘n’ particles can be expressed as follows: 

Consider an n-particle system in which molecules communicate with one another at an average distance ‘r’, owing to mutual gravitational attraction; there are n(n–1)/2 such interactions, and the system’s potential energy is equal to the sum of the potential energies of all pairs of particles, i.e.

US=12Gn(n-1)m2r2

Some important questions

Question 1: Find the gravitational potential energy of a body weighing 20Kg and is 320m above the ground.

Solution:

We know from the question that:

Mass = 20 Kg and Height = 30 m

G.P.E is given as,

U = m × g × h

= 20 Kg 9.8 m/s2 × 30 m = 5880 J.

Question 2: A bowling ball that has a weight of 2.2 kg falls 50 metres to the ground below. And find the ball’s gravitational potential energy when it reaches the bottom.

Solution:

According to the question, 

m = 2.2 Kg

h = 50 m

G.P.E is given as,

U = m × g × h

GPE = (2.2 kg)(9.8 m/s2)(50 m) = 1078 J.

Question 3: From a height of 12 metres, a body weighing 2 kg free falls. Calculate the amount of work done by gravity as well as the difference in gravitational potential energy. Assume a gravitational acceleration of 10 m/s2.

Solution:

We know that:

W = mgh

Thus, 

W = 2 × 12 × 10 = 240 N

This equation defines work done and is equal to the change in gravitational potential energy.

As a result, the gravitational potential energy equals 240 Joule.

Conclusion

Thus in these notes, we have learnt that the energy owned or obtained by an object as a result of a change in its position while in a gravitational field is known as gravitational potential energy. We have further studied and answered some important questions on gravitational potential energy.