If the velocity of an object moving at a certain height is increase 4 times, then what will be the change in the potential energy of the object?

Answer: Option A

Let's understand potential energy first.
Potential energy (PE) is the energy an object has because of its position or height.
The formula for potential energy is: PE = mgh,
where:
m is the mass of the object,
g is the acceleration due to gravity (which is constant), and
h is the height of the object.

Notice that the velocity of the object doesn't appear in the formula for potential energy.
Potential energy depends only on the mass, gravity, and height.
Changing the velocity of the object at a certain height does not change its height.

Since the height remains the same, and the mass and gravity are also constant, the potential energy will not change.

Therefore, the correct answer is A: Potential energy will be constant.