The masses and radii of the earth and moon are $${{M}_{1}},\,{{R}_{1}}$$ and $${{M}_{2}},\,{{R}_{2}}$$ respectively. Their centres are distance d apart. The minimum velocity with which a particle of mass m should be projected from a point midway between their centres so that it escapes to infinity is [MP PET 1997]

Question

The masses and radii of the earth and moon are $${{M}_{1}},\,{{R}_{1}}$$ and $${{M}_{2}},\,{{R}_{2}}$$ respectively. Their centres are distance d apart. The minimum velocity with which a particle of mass m should be projected from a point midway between their centres so that it escapes to infinity is   [MP PET 1997]

TuteeHUB · Accepted Answer

$$2\sqrt{\frac{2G}{d}({{M}_{1}}+{{M}_{2}})}$$

TuteeHUB · Answer

$$2\sqrt{\frac{G}{d}({{M}_{1}}+{{M}_{2}})}$$

TuteeHUB · Answer

$$2\sqrt{\frac{Gm}{d}({{M}_{1}}+{{M}_{2}})}$$

TuteeHUB · Answer

$$2\sqrt{\frac{Gm({{M}_{1}}+{{M}_{2}})}{d({{R}_{1}}+{{R}_{2}})}}$$

1.	The masses and radii of the earth and moon are \[{{M}_{1}},\,{{R}_{1}}\] and \[{{M}_{2}},\,{{R}_{2}}\] respectively. Their centres are distance d apart. The minimum velocity with which a particle of mass m should be projected from a point midway between their centres so that it escapes to infinity is [MP PET 1997]
A.	\[2\sqrt{\frac{G}{d}({{M}_{1}}+{{M}_{2}})}\]
B.	\[2\sqrt{\frac{2G}{d}({{M}_{1}}+{{M}_{2}})}\]
C.	\[2\sqrt{\frac{Gm}{d}({{M}_{1}}+{{M}_{2}})}\]
D.	\[2\sqrt{\frac{Gm({{M}_{1}}+{{M}_{2}})}{d({{R}_{1}}+{{R}_{2}})}}\]
Answer» B. \[2\sqrt{\frac{2G}{d}({{M}_{1}}+{{M}_{2}})}\]

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