Question:
The potential energy of $ 4 $ -particles each of mass $ 1\,kg $ placed at the four vertices of a square of side length $ 1\,m $ is
The potential energy of $ 4 $ -particles each of mass $ 1\,kg $ placed at the four vertices of a square of side length $ 1\,m $ is
Updated On: Jun 14, 2022
- $ + 4.0\, G $
- $ -7.5\,G $
- $ -5.4\,G $
- $ + 6.3 \,G $
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The Correct Option is C
Solution and Explanation
Here, $AB=BC=CD=DA=1\,m$
$BD=AC$
$=\sqrt{1^{2}+1^{2}}$
$=\sqrt{2}m$
Total potential energy
$+\left[\frac{-G\times1\times1}{DA}\right]+\left[\frac{-G\times1\times1}{BD}\right]+\left[\frac{-G\times1\times1}{AC}\right]$
$=4\times\left[\frac{-G\times1\times1}{1}\right]+2\left[\frac{-G\times1\times1}{\sqrt{2}}\right]$
$=-5.4\,G$
$BD=AC$
$=\sqrt{1^{2}+1^{2}}$
$=\sqrt{2}m$
Total potential energy
$+\left[\frac{-G\times1\times1}{DA}\right]+\left[\frac{-G\times1\times1}{BD}\right]+\left[\frac{-G\times1\times1}{AC}\right]$
$=4\times\left[\frac{-G\times1\times1}{1}\right]+2\left[\frac{-G\times1\times1}{\sqrt{2}}\right]$
$=-5.4\,G$
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Concepts Used:
Potential Energy
The energy retained by an object as a result of its stationery position is known as potential energy. The intrinsic energy of the body to its static position is known as potential energy.
The joule, abbreviated J, is the SI unit of potential energy. William Rankine, a Scottish engineer, and physicist coined the word "potential energy" in the nineteenth century. Elastic potential energy and gravitational potential energy are the two types of potential energy.
Potential Energy Formula:
The formula for gravitational potential energy is
PE = mgh
Where,
- m is the mass in kilograms
- g is the acceleration due to gravity
- h is the height in meters
Types of Potential Energy:
Potential energy is one of the two main forms of energy, along with kinetic energy. There are two main types of potential energy and they are:
- Gravitational Potential Energy
- Elastic Potential Energy