Energy due to position of a particle is given by, U=(α√(y))/(y+β), where αand βare constants, y

Step 1: The given energy equation is $U=frac{alpha sqrt{y}}{y+beta}$, where $U$ is energy, $y$ i

Energy due to position of a particle is given by,...

Energy due to position of a particle is given by, $U=\frac{\alpha \sqrt{y}}{y+\beta}$, where $\alpha$ and $\beta$ are constants, $y$ is distance. The dimensions of $(\alpha \times \beta)$ are (A) $\left[M^{0} L T^{0}\right]$ (B) $\left[M^{1 / 2} L^{3 / 2} T^{-2}\right]$ (C) $\left[M^{0} L^{-7 / 2} T^{0}\right]$ (D) $\left[M L^{7 / 2} T^{-2}\right]$

Energy due to position of a particle is given by, $U=\frac{\alpha \sqrt{y}}{y+\beta}$, where $\alpha$ and $\beta$ are constants, $y$ is distance. The dimensions of $(\alpha \times \beta)$ are
(A) $\left[M^{0} L T^{0}\right]$
(B) $\left[M^{1 / 2} L^{3 / 2} T^{-2}\right]$
(C) $\left[M^{0} L^{-7 / 2} T^{0}\right]$
(D) $\left[M L^{7 / 2} T^{-2}\right]$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Dimensional Analysis

Dimensional analysis is a method used to deduce the relationships between physical quantities by comparing their dimensions. It involves equating the dimensions on both sides of an equation to ensure that the equation is physically meaningful. This process helps in identifying the units of unknown constants or in verifying the consistency of derived equations.

Dimensional Homogeneity

Dimensional homogeneity is the principle that every additive term in a physical equation must have the same dimensions. This requirement ensures that equations are valid and consistent because only quantities with identical dimensions can be physically added or compared. It is crucial when dealing with sums in the denominator or other composite expressions.

Physical Dimensions of Energy

The study of the physical dimensions of energy involves understanding that energy is expressed in terms of mass, length, and time (typically [M L² T?²]). When energy appears in an equation, the dimensions of all other quantities and constants involved must combine in a way that reproduces these energy dimensions. This concept is essential for determining the dimensions of unknown constants in energy expressions.

Please give Ace some feedback