1.

calculate the gravitaional intensity and graviational potential at a location which is from the surface of the Earth at a height `4` times the radius of the surface. `R_(e) = 6400 km`, `G = 6.67 xx 10^(-11) Nm^(2) kg^(-2) , M_(e) = 6 xx 10^(24) kg`.

Answer» `I = (GM)/((R + h)^(2)) = (GM)/((R + 4R)^(2)) = (GM)/(25R^(2))`
`= ((6.67 xx 10^(-11)) xx (6 xx 10^(24)))/(25 xx (6.4 xx 10^(6))^(2)) = 0.39 N//kg`
`V = - (GM)/((R + h)) = - (6.67 xx 10^(-11) xx 6 xx 10^(24))/(5 xx 6.4 xx 10^(6))`
`= - 1.25 xx 10^(7) J kg^(-1)`


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