Question

The period of revolution of Jupiter around the sun is 12 times the period of revolution of the earth around the sun. The distance between the Jupiter and sun is n times the distance between the earth and sun. Then the value of n is

• A. (144)3/2
• B. (144)2/3
• C. $ \sqrt[3]{144} $
• D. $ \sqrt[4]{144} $

Answer 1

Answer: (C)

The time period the earth around the sun $ {{T}^{2}}\propto {{a}^{3}} $ ?(i) According to the question $ {{(12T)}^{2}}\propto {{(na)}^{3}} $ ?(ii) $ \therefore $ $ \frac{{{(12T)}^{2}}}{{{T}^{2}}}=\frac{{{(na)}^{3}}}{{{a}^{3}}} $ or $ 144={{n}^{3}} $ or $ n=\sqrt[3]{144} $