The potential energy of a particle varies wit | vedclass

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

Question

(B) The principle of homogeneity of dimensions states that only quantities with the same dimensions can be added or subtracted.Since $B$ is added to $

Vedclass · Accepted Answer

$M^1 L^{3/2} T^{-2}$

Vedclass · Answer

(B) The principle of homogeneity of dimensions states that only quantities with the same dimensions can be added or subtracted.Since $B$ is added to $x^2$,the dimensions of $B$ must be equal to the dimensions of $x^2$.$[B] = [x^2] = L^2$.The potential energy $U$ has the dimensions of work,which is $[U] = M L^2 T^{-2}$.The given equation is $U = \frac{A \sqrt{x}}{x^2 + B}$.Considering the dimensions of the denominator,$[x^2 + B] = L^2$.Thus,$[U] = \frac{[A] [x]^{1/2}}{L^2}$.Substituting the dimensions: $M L^2 T^{-2} = \frac{[A] L^{1/2}}{L^2}$.$[A] = (M L^2 T^{-2}) 	imes (L^{3/2}) = M L^{7/2} T^{-2}$.Now,calculate the dimensions of $A/B$:$[A/B] = \frac{M L^{7/2} T^{-2}}{L^2} = M L^{7/2 - 2} T^{-2} = M L^{3/2} T^{-2}$.

The potential energy of a particle varies with distance $x$ from a fixed origin as $U = \frac{A\sqrt{x}}{x^2 + B}$,where $A$ and $B$ are dimensional constants. Find the dimensional formula for $A/B$.

Similar Questions

Given that $v$ is the speed,$r$ is the radius,and $g$ is the acceleration due to gravity. Which of the following is dimensionless?

If $L$,$C$,and $R$ denote the inductance,capacitance,and resistance respectively,the dimensional formula for $C^{2}LR$ is

Force $F$ is given in terms of time $t$ and distance $x$ by $F = a \sin(ct) + b \cos(dx)$. Then the dimension of $a/b$ is:

The velocity $v$ (in $cm/sec$) of a particle is given in terms of time $t$ (in $sec$) by the relation $v = at + \frac{b}{t + c}$. The dimensions of $a, b,$ and $c$ are:

If $C$ (the velocity of light),$h$ (Planck's constant),and $G$ (gravitational constant) are taken as fundamental quantities,then the dimensional formula of mass is

Vedclass Test Series

Exam Paper Generator

Online Exam Module