The potential energy of a particle varies with distance x

The correct option is B M 1 L 11 2 T − 2 Lets find out dimensions of B first: Now in the equation given, we have x 2 + B in the denominator. So dimensions of B must be equal to dimensions of x 2. ∴ [ B ] = [ L 2 ] Now we will find dimensions of A: U = A x 1 / 2 x 2 + B [ M L 2 T − 2 ] = [ A ] [ L 1 / 2 ] [ L 2 ] [ A ] = [ M L 2 T − 2 ] [ L 2 ] [ L 1 / 2 ] So, the dimensions of A × B are: [ A ] × [ B ] = [ M L 2 T − 2 ] [ L 2 ] [ L 1 / 2 ] . [ L 2 ]

https://phys.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FUniversity_Physics%2FBook%253A_University_Physics_(OpenStax)%2FBook%253A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)%2F08%253A_Potential_Energy_and_Conservation_of_Energy%2F8.05%253A_Potential_Energy_Diagrams_and_Stability Expand/collapse global hierarchy • Home • Bookshelves • University Physics • Book: University Physics (OpenStax) • University Physics I - Mechanics, Sound, Oscillations, and Waves (OpenStax) • 8: Potential Energy and Conservation of Energy • 8.5: Potential Energy Diagrams and Stability Expand/collapse global location \( \newcommand\) • • • • • • • Learning Objectives • Create and interpret graphs of potential energy • Explain the connection between stability and potential energy Often, you can get a good deal of useful information about the dynamical behavior of a mechanical system just by interpreting a graph of its potential energy as a function of position, called a potential energy diagram. This is most easily accomplished for a one-dimensional system, whose potential energy can be plotted in one two-dimensional graph—for example, U(x) versus x—on a piece of paper or a computer program. For systems whose motion is in more than one dimension, the motion needs to be studied in three-dimensional space. We will simplify our procedure for one-dimensional motion only. First, let’s look at an object, freely falling vertically...

healthy restaurants near the question is to potential energy of a particle varies with distance x from a fixed origin as you equals to a root x divided by X + b and B are dimension constant then find the dimension formula for a and P your potential energy is a root x protected nothing but x to the power 1 by 2 divided by X square + b x is distance and NTR dimensional constant to hear from the situation we can say that the dimension of B are similar to that of the dimension of x square we can say that dimension of is equal to dimension of dimension of the will be equal to as access distance will be l determination of extra will be there we can see that the dimension of nothing now to calculate the dimensions of a we can write the equation of a as will be equal to in 2 to the power 1 by 2 Tu Hi Hai missions of you that is energy for the unit of energy in joule into the unit of x square + b

Learning Objectives By the end of this section, you will be able to: • Create and interpret graphs of potential energy • Explain the connection between stability and potential energy Often, you can get a good deal of useful information about the dynamical behavior of a mechanical system just by interpreting a graph of its potential energy as a function of position, called a potential energy diagram. This is most easily accomplished for a one-dimensional system, whose potential energy can be plotted in one two-dimensional graph—for example, U( x) versus x—on a piece of paper or a computer program. For systems whose motion is in more than one dimension, the motion needs to be studied in three-dimensional space. We will simplify our procedure for one-dimensional motion only. First, let’s look at an object, freely falling vertically, near the surface of Earth, in the absence of air resistance. The mechanical energy of the object is conserved, [latex] E=K+U, [/latex] and the potential energy, with respect to zero at ground level, is [latex] U(y)=mgy, [/latex] which is a straight line through the origin with slope [latex] mg [/latex]. In the graph shown in x-axis is the height above the ground y and the y-axis is the object’s energy. The line at energy E represents the constant mechanical energy of the object, whereas the kinetic and potential energies, [latex] . [/latex] You can see how the total energy is divided between kinetic and potential energy as the object’s height chan...