A particle of mass $$50$$ g is kept on the surface of a uniform sphere of mass $$120$$ kg and radius $$50$$ cm. Find the work to be done in ×$$10$$−$$10J$$ against the gravitational force between them to take the particle far away from the sphere. Take $$G=6.67$$×$$10$$−$$11Nm2kg$$−$$2$$.

Question

A particle of mass $$50$$ g is kept on the surface of a uniform sphere of mass $$120$$ kg and radius $$50$$ cm. Find the work to be done  in ×$$10$$−$$10J$$ against the gravitational force between them to take the particle far away from the sphere. Take $$G=6.67$$×$$10$$−$$11Nm2kg$$−$$2$$.

Infinity Learn · Accepted Answer

Here, $$M=120kg$$;$$m=50g=0.05kg$$           $$R=50cm=0.5m$$ and $$G=6.67$$×$$10$$−$$11Nm2kg$$−$$2Now$$, initial potential energy of the system of sphere and particle,$$Ui=$$−$$GMmR=$$−$$6.67$$×$$10$$−$$11$$×$$120$$×$$0.050.5=$$−$$8.0$$×$$10$$−$$10JWhen$$ the particle is far away from the sphere, the potential energy of the system will be zero i.e. Uf $$=0Therefore$$, required work done,                  $$W=Uf$$−$$Ui=0$$−−$$8.0$$×$$10$$−$$10=8.0$$×$$10$$−$$10J$$

Gravitational potential and potential energy

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A particle of mass 50 g is kept on the surface of a uniform sphere of mass 120 kg and radius 50 cm. Find the work to be done $(in \times 10^{- 10} J)$ against the gravitational force between them to take the particle far away from the sphere. Take $G = 6 .67 \times 10^{- 11} {Nm}^{2} {kg}^{- 2}$ .

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Gravitational potential and potential energy

Remember concepts with our Masterclasses.

A particle of mass 50 g is kept on the surface of a uniform sphere of mass 120 kg and radius 50 cm. Find the work to be done in ×10−10J against the gravitational force between them to take the particle far away from the sphere. Take G=6.67×10−11Nm2kg−2.

Ready to Test Your Skills?

free study material

A particle of mass 50 g is kept on the surface of a uniform sphere of mass 120 kg and radius 50 cm. Find the work to be done $(in \times 10^{- 10} J)$ against the gravitational force between them to take the particle far away from the sphere. Take $G = 6 .67 \times 10^{- 11} {Nm}^{2} {kg}^{- 2}$ .