Question

56) if you were licated haldway between earb and the moon what acceleration would you have toward earth? the earth-moon separatjon js 60 earth raddi (ignore the gravitational dorce of the moon because it is much less than earths)

57) A solid lead sphere of raduus 10 m about 66 ft across has a mass if about 57 million kg if two of these soveres are floating un deep soace wirh theie cenrers 20 m apart the gravitational attraction between the spheres is only 540 N (about 120 lb) how large would the gravitational force be if the distance between the centers of the two spheres were trippled?

Answer 1

Solution :-

These two problems are based on the concept of newton's law of gravitation according to which, the force of attraction between two masses m₁ and m₂ separated by a distance r is given by the formula as : F=Gm₁m₂/r². Here we also need Newtons second law of motion according to which net force on any body of mass m is given by : F=ma, where a is acceleration of body and according to question 56 only earth is exerting force on mass at P, so acceleration = Force/mass. We can see that newtons gravitation force is inversely proportional to r², question 57 can be solved directly keeping in mind that all values are same except for r (which is 3r=60 now), so 540/9 approximately gives 60 N. Please find the detailed solution below and feel free to ask any doubt you face while understanding my solution. I would be happy to help.