A tunnel is dug along the diameter of the earth (radius$$ R and mass $$M). There is a particle of mass 'm' at the centre of the tunnel. The minimum velocity given to the particle so that it just reaches to the surface of the earth is

Question

A tunnel is dug along the diameter of the earth (radius$$ R and mass  $$M). There is a particle of mass 'm'  at the centre of the tunnel. The minimum velocity given to the particle so that it just reaches to the surface of the earth is

Infinity Learn · Accepted Answer

Given Mass of Earth $$=MRadius$$ of Earth $$=RLet$$ the minimum speed imparted to the particle of mass m  so that it just reaches surface of earth is  v.Applying the principle of conservation of energy,$$12mv2+$$−$$32GMRm=$$−$$GMRm+0$$  $$12v2=$$−$$GMR+32GMR=GMR$$ , we get  $$v=GMR$$.Therefore, the correct answer is (A).

A tunnel is dug along the diameter of the earth (radius R and mass M). There is a particle of mass $' m'$ at the centre of the tunnel. The minimum velocity given to the particle so that it just reaches to the surface of the earth is

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A tunnel is dug along the diameter of the earth (radius R and mass M). There is a particle of mass 'm' at the centre of the tunnel. The minimum velocity given to the particle so that it just reaches to the surface of the earth is

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A tunnel is dug along the diameter of the earth (radius R and mass M). There is a particle of mass $' m'$ at the centre of the tunnel. The minimum velocity given to the particle so that it just reaches to the surface of the earth is