Question

At what height from the surface of earth the gravitation potential and the value of g are –5.4×107Jkg–2 and 6.0ms–2 respectively ? Take the radius of earth as 6400km :

Answer 1

Case 1:

When mgh = 5.4 × 10^4 J

$mgh = 5.4 \times {10}^{7} \\ \\ 1 \times 9.8 \times h = 5.4 \times {10}^{7} \: \: \: \: \: (let \: the \: mass \: be \: 1kg) \\ \\ h = \frac{5.4 \times {10}^{7} }{98 \times {10}^{ - 1} } \\ \\ h = 0.055 \times {10}^{8} \\ h = 55 \times {10}^{5} m$





Case 2:

When g = 6m/s²

$g = \frac{Gm}{ {r}^{2} } \\ \\ 6 = \frac{6.67 \times {10}^{ - 11} \times 5.97 \times {10}^{24} }{ {r}^{2} } \\ \\ {r}^{2} = \frac{39.81 \times {10}^{13} }{0.06 \times {10}^{2} } \\ \\ {r}^{2} = 663.5 \times {10}^{11} \\ \\ r = \sqrt{663.5 \times {10}^{11} } \\ \\ r = 8145550.93 \: m \\ \\ distance \: above \: earths \: surface = r - earths \: radius \\ \\ h = 8145550.93 - 6400000 \\ \\ h = 1745550.93 \: m \: or \: 1745.550 \: km \:$