The masses and radii of the earth and moon are $$M1$$, $$R1$$ 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

Question

The masses and radii of the earth and moon are $$M1$$, $$R1$$ 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

Infinity Learn · Accepted Answer

Gravitational potential energy at mid $$pointU=U1+U2=$$−$$GmM1d/2+$$−$$GmM2d/2=$$−$$Gmd/2M1+M2=$$−$$2GmdM1+M2$$[m $$=$$ mass of particle]So, for projecting particle from mid point to infinityKE $$=$$ | $$PE$$ |⇒ $$12mv2=2$$ $$Gmd(M1+M2)$$                               ⇒ $$v=2G$$ $$(M1+M2)d$$

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

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The masses and radii of the earth and moon are 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 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