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 $=3.85\times {10}^8-3.46\times {10}^8$ $=3.9\times {10}^{7}m$