Question

Write the expression for the gravitational potential energy explaining the meaning of the symbols used.

Answer 1

Hint: To solve the question given above we will first discuss what is gravitational potential energy then we will find the expression of gravitational potential energy after that we will explain the symbols used in the formula of gravitational potential energy.

Complete step-by-step solution:
In order to solve the above question where we have to write the expression for the gravitational potential energy and explain the meaning of the symbols let us first discuss what is gravitational potential energy?
Gravitational potential energy is defined as the energy possessed or acquired by any object by the virtue of its change in position when it is present in the gravitational field.
It is usually given by the symbol U.
Now, we are aware of what is gravitational potential energy so, let us now check what is the expression of gravitational potential energy?
So, Let us consider an object of mass m which is being lifted to a certain height h. The body is lifted above the ground so it is lifted against gravity. Now, force is required to lift the object which is F is equal to the force of gravity.
As we know energy is defined as the capability of doing work. So, we know that energy is equal to work done. That's why here we will find the work done by the force on the weight.
We know that,
\[Work\_done=Force\times displacement\] - - - - - -Equation 1
Here in the expression of gravitational potential energy, displacement is the height at which the body is lifted that is h and force is the force done by the weight.
Since, we know that
\[Force=Mass\times Acceleration\]
But in this case, we use acceleration due to gravity is g
\[F=mg\]
Now put this value of force in Equation 1, we get
\[Work=mg\times h\]
\[\therefore Work=mgh\]
Let us assume this work can be represented as W.
\[W=mgh\]
This work done against gravity is stored in the form of gravitational potential energy which is represented by U.
\[\therefore U=mgh\]
Where m is mass of the body.
g is acceleration due to gravity.
h is the height of the object upto which is taken under gravity.

Note: In the above question we got to know that work done is equal to the energy possessed by the body as we know that energy is defined as the capability of doing work. Also remember that work is against the gravity so, in place of acceleration we will use acceleration due to gravity.