Question

A planet moves around the sun in nearly circular orbit. Its time period of revolution ‘T’
depends upon radius ‘r’ of orbit, mass ‘M’ of the sun and the gravitational constant ‘G’. Show
dimensionally that T 2 α r 3

Answer 1

Given:

Time period of revolution ‘T’  of planet depends upon radius ‘r’ of orbit, mass ‘M’ of the sun and the gravitational constant ‘G.

To Prove:

Dimensionally show that T² ∝ r³.

Calculation:

- Dimensions of the given quantities are given as:

T = [T]

r = [L]

M = [M]

G = [M⁻¹L³T⁻²]

- It is given that T depends upon r, M, and G.

i.e., T ∝ r^a M^b G^c

⇒ [T] = [L]^a [M]^b [M⁻¹L³T⁻²]^c

⇒ [T] = [M]^(b-c) [L]^(a+3c) [T]^-2c

On comparing, we get:

a = 3/2, b = 1/2 and c = -1/2

⇒ T ∝ r^3/2

⇒ T² ∝ r³

Hence, proved.

Answer 2

hope this will help you and marks it as brainlist plzzzzzzzzz also follow me guys.