Question

The change in gravitational potential energy per unit space (distance) of a body represent:
A) Mass.
B) Kinetic energy.
C) Linear momentum.
D) Weight.

Answer 1

Hint:Potential energy is defined as the energy stored in an object due to its position with respect to a zero position. Gravitational potential is defined as the potential energy of a large object in relation to other objects due to the gravity.

Formula used:The formula of the gravitational energy is given by,
$U = mgh$
Where potential energy is U, the mass of the body is m, the height from the ground is h and the acceleration due to gravity is g.

Complete step by step answer:
It is asked in the problem that what is the change in gravitational potential energy per unit space and we need to select the correct option here.
The gravitational potential energy is defined as the energy possessed by a body due to its position comparative to a zero position. The change of gravitational potential energy per unit space of a body is the change of the potential energy with the change in the height.
The formula of the gravitational energy is given by,
$ \Rightarrow U = mgh$
Where potential energy is U, the mass of the body is m, the height from the ground is h and the acceleration due to gravity is g.
Now the change of gravitational potential energy with respect to change in height is given by,
$ \Rightarrow \dfrac{{dU}}{{dh}} = \dfrac{{mgh}}{h}$
$ \Rightarrow \dfrac{{dU}}{{dh}} = mg$
The gravitational potential energy per unit of the space is equal to$\dfrac{{dU}}{{dh}} = mg$. So the gravitational potential energy per unit of the space is weight.

The correct option for this problem is option D.

Note:It is advisable for students to remember the formula of the gravitational energy as it is helpful for solving these kinds of problems. The change of gravitational potential energy with respect to unit space i.e. change in height is asked in the problem.