Physics, asked by Damanpreet1125, 11 months ago

show that following equation is dimensionally correct F=2GMm/(R+h)^2

Answers

Answered by tanishka427varshney
9

Explanation:

hope this will help u...

Attachments:
Answered by probrainsme101
0

Given:

The given equation is,

F = 2GMm/(R+h)²

Find:

Showing that the equation is dimensionally correct.

Solution:

For an equation to be dimensionally correct, the dimensions on the left-hand side should be equal to the dimensions on the right-hand side.

Given,

F = 2(GMm)/(R+h)²

where F = Force

G = Gravitational constant

M and m are masses.

R and h are distances.

We will now write the dimensions.

Dimensions of F = [M L T⁻²]

∴ Dimensions on the left-hand side,

L.H.S. =  [M L T⁻²]

Now, dimensions of G = [M⁻¹ L³ T⁻²]

Dimensions of M = [M L⁰ T⁰]

Dimensions of m = [M L⁰ T⁰]

Dimensions of R = [M⁰ L T⁰]

Dimensions of h = [M⁰ L T⁰]

Dimensions of (R+h) =  [M⁰ L T⁰]

Putting the values on the right-hand side, we have

Dimensions on R.H.S. = { [M⁻¹ L³ T⁻²][M L⁰ T⁰][M L⁰ T⁰] } /  [M⁰ L T⁰]²

                                     = [M L³ T⁻²]/[M⁰ L² T⁰]

                                     = [M¹⁻⁰ L³⁻² T⁻²⁻⁰]

                                     = [M L T⁻²]

Clearly, Dimensions on L.H.S. = Dimensions on R.H.S.

[M L T⁻²] = [M L T⁻²]

Hence, the given equation is dimensionally correct.

Hence proved.

#SPJ2

Similar questions