Question

The energy of a body is given by
E = (Ax^1/2)/ (x^2 + B) .
Here, x is the distance and A,B are constants.What is the dimensional formula of AB ?

Answer 1

i didnt understand plz re type

Answer 2

Answer:

The dimensional formula of AB is $[M\;L^{11/2}\;T^{-2}]$

Explanation:

Given, the expression of energy of a body is:-

$E =\frac{A\sqrt{x} }{x^2+B}$                                                                              ...................(1)

where A, B are constants and x is the distance.

Consider x in the unit of meters.

The two quantities can be added only if they have same unit. Therefore the units of B will be same as x².

The unit of B is also m².

Therefore, the dimensional formula of B = [L²]

Now, the energy can be taken in Joule. We now that one Joule is equal to 1 Kgm²s⁻².

Substitute the units in expressions (1);-

$Kgm^2s^{-2} =\frac{A\times m^{1/2}}{m^2+m^2}$

$A = \frac{Kg\;m^2s^{-2}\times m^2}{m^{1/2}}$

$A = Kg\; m^{7/2}s^{-2}$

Therefore, the dimensional formula of A = $[M\; L^{7/2}\;T^{-2}]$

So, the dimensional formula of AB $=[M\; L^{7/2}\;T^{-2}] [L^2]$

Therefore, dimensional formula of AB  $=[M\;L^{11/2}\;T^{-2}]$

To know more about "Dimensional formula of energy"

https://brainly.in/question/48907921

To know more about "Dimensional formula for average velocity"

https://brainly.in/question/5123619