The potential energy of a particle varies with distance x from a fixed origin as V = frac{{Asqrt x }}{{x + B}},where A and B

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

d Dimension of $\mathrm{A}$ is equals to dimension of $\frac{U\left(x+B\right)}{\sqrt{x}}$ or $\left[M L^{2} T^{-2}\right] \cdot \frac{L}{L^{\frac{1}{2}}}$ i.e $\left[M L^{\frac{5}{2}} T^{-2}\right]$ And dimension of $\mathrm{B}$ is equals square of $x$ that is $\left[L\right]$ (because two quantities can be added only when their dimension is the same) So dimension of $A . B$ will be $\left[M L^{\frac{7}{2}} T^{-2}\right]$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

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

A$ML^{5/2} T^{-2}$
B$M^1 L^2 T^{-2}$
C$M^{3/2} L^{3/2} T^{-2}$
D$M^1 L^{7/2} T^{-2}$

AIIMS 2017, Diffcult

STD 11 Science
JEE
STD 11 - 1. units,dimensions and measurement
Physics

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Download App

Similar Questions

1
Whose dimensions is $M{L^2}{T^{ - 1}}$
View Solution
2
The pitch of the screw gauge is $1\, mm$ and there are $100$ divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies $8$ divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while $72^{\text {nd }}$ division on circular scale coincides with the reference line. The radius of the wire is.........$mm$
View Solution
3
If $x$ and $a$ stand for distance then for what value of $n$ is given equation dimensionally correct the eq. is $\int {\frac{{dx}}{{\sqrt {{a^2}\, - \,{x^n}} \,}}\, = \,{{\sin }^{ - 1}}\,\frac{x}{a}} $
View Solution
4
The dimensions of $C{V^2}$ matches with the dimensions of
View Solution
5
A unitless quantity?
View Solution
6
Dimensional formula $M{L^{ - 1}}{T^{ - 2}}$ does not represent the physical quantity
View Solution
7
The radius of a sphere is measured to be $(7.50 \pm 0.85) \,cm .$ Suppose the percentage error in its volume is $x$. The value of $x$, to the nearest integer is .....$\%$
View Solution
8
Which of the following units denotes the dimensions $\frac{{M{L^2}}}{{{Q^2}}}$, where $Q$
denotes the electric charge?
View Solution
9
Given below are two statements :

$Statement$ $(I)$ : Planck's constant and angular momentum have same dimensions.

$Statement$ $(II)$ : Linear momentum and moment of force have same dimensions.

In the light of the above statements, choose the correct answer from the options given below :
View Solution
10
If energy $(E),$ velocity $(V)$ and time $(T)$ are chosen as the fundamental quantities, the dimensional formula of surface tension will be
View Solution

Download our appand get started for free

Similar Questions

Download our app
and get started for free