Question

A horse drinks water from a cubical container of side $1\,m$ with water filled upto $1\,m$. The level of the stomach of the horse is at $2\,m$ from the ground. Assume that all the water drunk by the horse is at a level of $2\,m$ from the ground, then the minimum work done by the horse in drinking the entire water of the container is? \[\left( {Take\;{\rho _{water}} = 1000kg{m^{ - 3}}\;and\;g = 10m{s^2}} \right)\]
A. 10 KJ
B. 20 KJ
C. 15 KJ
D. None of these

Answer 1

Hint:Potential energy is the energy that an item has as a result of its location in relation to other items. Potential energy is frequently related to restoring forces like springs and gravity. An external force that acts against the force field of the potential performs the operation of stretching a spring or lifting a load. The force field, which is considered to be stored as potential energy, stores this work.

Formula used:
$E = mgh$
Here, $m$ = mass, $g$ = acceleration due to gravity and $h$ = height.

Complete step by step answer:
Potential energy is the energy that an item has due to its location in relation to other objects, internal tensions, electric charge, or other causes. The gravitational potential energy of an item, which is determined by its mass and distance from another object's centre of mass, the elastic potential energy of a stretched spring, and the electric potential energy of an electric charge in an electric field are all examples of potential energy.

The joule, denoted by the letter J in the International System of Units (SI), is the SI's energy unit. Water has a mass of $m$ =\[1 \times {10^3}\] kg. Horse work entails an increase in potential energy,
$E = mgh$
$\Rightarrow E= (1 \times {10^3})(10)(1.5)$
$\Rightarrow E=15\,kJ$ is the increase in water's potential energy.

Forces and potential energy are inextricably related. If the work done by a force on a body moving from point A to point B is independent of the path between these points (if the work is done by a conservative force), the work done by this force measured from point A assigns a scalar value to every other point in space and defines a scalar potential field. In this scenario, the force may be described as the inverse of the potential field's vector gradient.
$ \therefore E = 15\,kJ$

Hence, the correct answer is option C.

Note:Don’t make any mistakes in writing the force. A closed form can be used to express a conservative force in differential geometry. The fact that all conservative forces are gradients of a potential field is mathematically justified.