Question

If r denotes the distance between the sun and the earth, then the angular momentum of the earth around the sun is proportional to 

(A) r^3/2 

(B) r 

(C) r^1/2 

(D) r²

Answer 1

Correct option: (C) r^1/2

Explanation:

angular momentum = mass × orbital velocity × radius

L = mVr

for earth,

L = M_E ∙ V_o ∙ r

L = M_E ∙ √[(GMS) / r] × r

where M_E = mass of earth

M_S = mass of sun

i.e  L = M_E ∙ √[(GMS × r²) / r]

 L ∝ √r

i.e. L ∝ r^1/2