Which of the following objects has the greatest amount of gravitational potential energy?
Answers
the heaviest of 2 objects at the same height has the greatest amount of gravitational potential energy.
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Your Question was incomplete. The complete Question is here:
Which of the following objects has the greatest amount of gravitational potential energy?
a. ball tossed horizontally
b. a ball rolling on the ground
c. ball on the 5th floor of a building
d. a ball on the 10th floor of a building
Concept:
Gravitational Potential Energy:
It is the energy attained by an object or a body due to a change in its position in the presence of a gravitational force field.
For small objects (w.r.t size of earth), the gravitational force acting on an object is assumed to be constant and pointing towards the earth's center. So the gravitational potential energy of a body changes when there is a change in the height of the body's center of mass from the earth's surface.
If the total mass of the body is 'm' and the acceleration due to gravity is 'g,' and the height above the reference(sea level) of the body is 'h,' then the change in gravitational potential energy of the object is given by
Gravitational Potential Energy (GPE) = m·g·h
Given:
Various conditions/cases and of a ball are given.
Find:
We need to find the case in which the ball has minimal gravitational potential energy.
Solution:
1) Assuming the gravitational potential energy at sea level is zero.
Case 1: Ball tossed horizontally
Here the initial height of the ball is not mentioned. So assuming that ball is initial at sea level. Now the ball has only initial horizontal velocity. So the ball will follow a parabolic trajectory going down. So the ball's potential energy continuously decreases from zero(initially).
Case 2: Ball rolling on the ground.
Assuming ground refers to a flat surface at sea level, the height of the ball w.r.t sea level never changes. The GPE of the ball, in this case, is zero.
Case 3: ball on the 5th floor of a building.
Let us assume the 5th floor is at a height h from sea level. Then the
GPE = m.g.h = mgh
Case 4: a ball on the 10th floor of a building.
If the height of the 5th floor is h, then that of the 10th floor will be 2h.
⇒ GPE = m.g.2h = 2mgh
∴ The correct answer is D)a ball on the 10th floor of a building. From all the above cases, the ball placed on the tenth floor of the building will have a greater GPE than other cases(subjected to assumptions).
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