NEET Sample Paper NEET Sample Test Paper-14

  • question_answer 17) The masses and radii of the earth and moon are\[{{M}_{1}},{{R}_{1}}\]and\[{{M}_{2}},{{R}_{2}},\]respectively. Their centres are at distance d apart. The minimum speed with which a particle of mass m should be projected from the mid-point between their centres, so that the particle goes out from the gravitational influence of both earth and moon, is

    A) \[2\sqrt{\frac{G({{M}_{1}}+{{M}_{2}})}{md}}\]           

    B) \[2\sqrt{\frac{G({{M}_{1}}+{{M}_{2}})}{d}}\]

    C)  \[2\sqrt{\frac{G({{M}_{1}}-{{M}_{2}})}{md}}\]

    D) \[2\sqrt{\frac{G({{M}_{1}}-{{M}_{2}})}{d}}\] 

    Correct Answer: B

    Solution :

    By the Law of conservation of energy \[-\frac{G{{M}_{1}}m}{d/2}-\frac{G{{M}_{2}}m}{d/2}+\frac{m{{v}^{2}}}{2}=0\] Where v is the sought velocity \[v=2\sqrt{\frac{G({{M}_{1}}+{{M}_{2}})}{d}}\] Hence, the correction option is [b].

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