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
A particular color of light has a wavelength of 663 nm. What is the energy possessed by the light?
(Planck’s constant $h = 6.63 \times 10^{-34}$ J·s; Velocity of light $c = 3 \times 10^8$ m/s)- KEAM - 2024
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Questions Asked in JEE Main exam
- Let \( \langle a_n \rangle \) be a sequence such that \( a_0 = 0 \), \( a_1 = \frac{1}{2} \), and \( 2a_{n+2} = 5a_{n+1} - 3a_n \).n= 0,1,2,3.... Then \( \sum_{k=1}^{100} a_k \) is equal to:
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- Given below are two statements:
Statement (I): NaCl is added to the ice at \( 0^\circ C \), present in the ice cream box to prevent the melting of ice cream.
Statement (II): On addition of NaCl to ice at \( 0^\circ C \), there is a depression in freezing point.
In the light of the above statements, choose the correct answer from the options given below:- JEE Main - 2025
- Colligative Properties
- Let P be the foot of the perpendicular from the point \( (1, 2, 2) \) on the line \[ \frac{x-1}{1} = \frac{y + 1}{-1} = \frac{z - 2}{2} \] Let the line \( \mathbf{r} = (-\hat{i} + \hat{j} - 2\hat{k}) + \lambda (\hat{i} - \hat{j} + \hat{k})\), \( \lambda \in \mathbb{R} \), intersect the line \(L\) at \(Q\). Then \( 2(PQ)^2 \) is equal to:
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- The area of the region bounded by the curves \( x(1 + y^2) = 1 \) and \( y^2 = 2x \) is:
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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