Question

find the depth at which the value of g us equal to the value of g at h =16 on the surface of earth
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Answer 1

Answer:

: At a point above the surface of earth, the gravitational potential is -5.12 × 107J/kg and the acceleration due to gravity is 6.4 m/s2. Assuming the mean radius of the earth to be 6400 km, calculate the height of this point above the earth's surfa

Answer 2

Answer:

12783.979949843 km (or) 16.020050156799 km

Explanation:

In this question we need to find the depth at which value of g is equal to value of g at 16 metres above the surface of earth

The value of g at h metres above the earth is given by : $gh = g\left[\frac{Re}{Re+h} \right] ^{2}$

Where:

Re = radius of earth

h = height

Gravity at 16 metres above the earth = $gh = 10\left[\frac{6400}{6400+16} \right] ^{2}$

= $gh = 10\left[\frac{6400}{6416} \right] ^{2}$

= $gh = 9.950 \ m/s^{2}$

Value of g at depth is given as:

$gd = g\left[\frac{R-d}{R} } \right] ^{2}$

9.950=$10\left[\frac{6400-d}{6400} } \right] ^{2}$

9.950=$10\left[\frac{40960000+d^{2}-12800d }{40960000} } \right]$

0.9950=$\left[\frac{40960000+d^{2}-12800d }{40960000} } \right]$

40755200=$\left[{40960000+d^{2}-12800d } \right]$

d²-12800d+2,04,800

By solving the above equation we get roots as:

Root 1 = 12783.979949843

Root 2 =16.020050156799

So the value of g can either be equal at a depth of 12783.979949843 km or 16.020050156799 km