A) 4R
B) 8 R
C) 2R
D) 6R
Correct Answer: D
Solution :
Key Idea: Where gravitational field due to earth and moon cancel each other, there the gravitational force is equal. From Newtons law of gravitational the force of attraction between any two material particles is given by \[h=\frac{5}{4}D\] where \[mgh=\frac{1}{2}m{{v}^{2}}\] are masses r is the distance between the two. Since gravitation field cancel each other the force of attraction is equal and opposite. \[\Rightarrow \] \[v=\sqrt{2gh}\] \[v=\sqrt{5g\frac{D}{2}}\] \[\sqrt{5g\frac{D}{2}}=\sqrt{2gh}\] \[\Rightarrow \] Taking square root of the above expression, we have \[h=\frac{5}{4}D\] \[\lambda =\frac{\log 2}{{{T}_{1/2}}}=\frac{0.693}{{{T}_{1/2}}}=\frac{0.693}{20}=0.03465per\min \] \[t=\frac{2.303}{\lambda }{{\log }_{10}}\frac{{{N}_{0}}}{N}\] \[{{t}_{1}}=\frac{2.303}{0.03465}{{\log }_{10}}\frac{100}{67}=11.6\min \] \[{{t}_{2}}=\frac{2.303}{0.03465}{{\log }_{10}}\frac{100}{33}=32\min \] Hence, distance of that point from moon is 6R.You need to login to perform this action.
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