The masses and radii of the earth and moon arc $$M1$$, $$R1$$ and $$M2$$, $$R2$$, 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

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Infinity Learn · Accepted Answer

Gravitational potential at mid $$pointV=$$−$$GM1d/2+$$−$$GM2d/2$$ Now,  $$PE$$$$=m$$×$$V=$$−$$2GmdM1+M2$$[m $$=$$ mass of particle]So, for projecting particle from mid point to $$infinityKE=$$|$$PE$$|⇒$$12mv2=2GmdM1+M2$$⇒$$v=2GM1+M2d$$

The masses and radii of the earth and moon arc M₁, R₁ and M₂, R₂, 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

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The masses and radii of the earth and moon arc M1, R1 and M2, R2, 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

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Ready to Test Your Skills?

free study material

The masses and radii of the earth and moon arc M₁, R₁ and M₂, R₂, 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