question_answer

There are two bodies of masses 100 kg and 10000 kg separated by a distance 1m. At what distance from the smaller body, intensity of gravitational field will be zero?

A)  \[\frac{1}{9}m\]                

B)         \[\frac{1}{10}m\]

C)  \[\frac{1}{11}m\]               

D)         \[\frac{10}{11}m\]

Correct Answer: C

Solution :

 Let at distance r from the smaller body, intensity of gravitational field becomes zero, then                 \[\frac{G\times 10000}{{{(1-r)}^{2}}}=\frac{G\times 100}{{{r}^{2}}}\]                 \[100\,\,{{r}^{2}}={{(1-r)}^{2}}\] \[\Rightarrow \]               \[10r={{(1-r)}^{2}}\] \[\Rightarrow \]               \[11r=1\] \[\Rightarrow \]               \[r=\frac{\mathbf{1}}{\mathbf{11}}\mathbf{m}\].