Question

At what distance from the centre of the moon, the intensity of gravitational field will be zero? Take masses of earth and moon as $ 5.98\times {{10}^{2r}}kg $ and $ 7.35\times {{10}^{22}}kg $ respectively and distance between moon and earth is $ 3.85\times {{10}^{8}}m. $

• A. Zero
• B. $ 3.85\times {{10}^{7}}m $
• C. $ 8\times {{10}^{8}}m $
• D. $ 3.46\times {{10}^{8}}m $

Answer 1

Answer: (B)

Let x be the distance of the point from the centre of earth whose gravitational intensity is zero. Therefore, $ \frac{G{{M}_{e}}}{{{x}^{2}}}=\frac{GMm}{{{(3.85\times {{10}^{8}}-x)}^{2}}} $ $ \frac{x}{(3.85\times {{10}^{8}}-x)}=\sqrt{\frac{{{M}_{e}}}{{{M}_{m}}}}=\sqrt{\frac{5.98\times {{10}^{24}}}{7.35\times {{10}^{22}}}}=9 $ $ \frac{x}{9}+x=385\times {{10}^{8}} $ $ x=\frac{9\times 385\times {{10}^{8}}}{10} $ $ x=3.46\times {{10}^{8}}m $ Distance from moon $ =3.85\times {{10}^{8}}-3.46\times {{10}^{8}} $ $ =3.9\times {{10}^{7}}m $