Potential energy function corresponding to conservative force is given as \(U(x, y, z) = \frac{3x^2}{2} + 5y + 6z\) then the force at \(x = 6\) is \(pN\). The value of \(p\) upto \(2\) its nearest integral value is
Solution and Explanation
The Correct Answer is : \(20\)
Top Questions on potential energy
- Match List I with List IIChoose the correct answer from the options given below:
LIST I LIST II A Isothermal Process I Work done by the gas decreases internal energy B Adiabatic Process II No change in internal energy C Isochoric Process III The heat absorbed goes partly to increase internal energy and partly to do work D Isobaric Process IV No work is done on or by the gas - JEE Main - 2023
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Questions Asked in JEE Main exam
The portion of the line \( 4x + 5y = 20 \) in the first quadrant is trisected by the lines \( L_1 \) and \( L_2 \) passing through the origin. The tangent of an angle between the lines \( L_1 \) and \( L_2 \) is:
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- Let \[ \vec{a} = 2\hat{i} + \alpha \hat{j} + \hat{k}, \quad \vec{b} = -\hat{i} + \hat{k}, \quad \vec{c} = \beta \hat{j} - \hat{k}, \] where \( \alpha \) and \( \beta \) are integers and \( \alpha \beta = -6 \). Let the values of the ordered pair \( (\alpha, \beta) \) for which the area of the parallelogram of diagonals \( \vec{a} + \vec{b} \) and \( \vec{b} + \vec{c} \) is \( \frac{\sqrt{21}}{2} \), be \( (\alpha_1, \beta_1) \) and \( (\alpha_2, \beta_2) \). Then \( \alpha_1^2 + \beta_1^2 - \alpha_2 \beta_2 \) is equal to:
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- Consider the system of linear equations \( x + y + z = 4\mu \), \( x + 2y + 2\lambda z = 10\mu \), \( x + 3y + 4\lambda^2 z = \mu^2 + 15 \), where \( \lambda, \mu \in \mathbb{R} \). Which one of the following statements is NOT correct?
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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