Question

A planet moves around sun in a circular orbit it's speed revolution (T) depends on radius of orbit (L) , mass of sun (M) and gravitional constant (G). deduce by method of dimensions of relation

Answer 1

hello friend..!!

according to the question , we should deduce the dimensional relation.

⇒ given speed of revolution (T) depends on radius(L) , mass (M) and gravitational constant (G)

⇒ T α Rᵃ Mᵇ Gⁿ

⇒ [M⁰L⁰T¹] = [L]ᵃ [M]ᵇ [M⁻¹L³T⁻²]ⁿ

⇒ [M⁰L⁰T¹]  = [ Mᵇ⁻ⁿ Lᵃ⁺³ⁿ T⁻²ⁿ ]

while comparing L.H.S and R.H.S

we get,

b-n = 0 , a+3n = 0 , -2n = 1 

therefore,

n=-1/2  , a = 3/2 and  b = -1/2

therefore,

T = $R^{ \frac{3}{2} }$ $M^{ \frac{-1}{2} }$ $G^{ \frac{-1}{2} }$


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hope it helps..!!