The potential energy U of a particle varies w | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The potential energy $U$ has dimensions of work or energy,which is $[ML^2T^{-2}]$.According to the principle of homogeneity of dimensions,only qua

Vedclass · Accepted Answer

$[ML^{5/2}T^{-2}], [L]$

Vedclass · Answer

(A) The potential energy $U$ has dimensions of work or energy,which is $[ML^2T^{-2}]$.According to the principle of homogeneity of dimensions,only quantities with the same dimensions can be added or subtracted. In the denominator,$x + B$,$x$ is a distance,so $B$ must also have the dimensions of length.Therefore,$[B] = [L]$.Now,substitute the dimensions into the equation:$[ML^2T^{-2}] = \frac{[A] \cdot [L^{1/2}]}{[L]}$$[ML^2T^{-2}] = [A] \cdot [L^{-1/2}]$$[A] = [ML^2T^{-2}] \cdot [L^{1/2}]$$[A] = [ML^{5/2}T^{-2}]$Thus,the dimensions of $A$ and $B$ are $[ML^{5/2}T^{-2}]$ and $[L]$ respectively. The correct option is $A$.

The potential energy $U$ of a particle varies with distance $x$ from a fixed origin as $U = \frac{A \sqrt{x}}{x + B}$,where $A$ and $B$ are constants. The dimensions of $A$ and $B$ are respectively

Similar Questions

Which of the following physical quantities has no dimensions?

Give the dimensional formula of surface tension.

Which one of the following quantities has dimensions different from the remaining three?

The dimensional formula ${M^0}{L^2}{T^{ - 2}}$ stands for

Vedclass Test Series

Exam Paper Generator

Online Exam Module