At what height from the surface of earth the gravitation potential and the value of g are -5.4 \times 107 J kg-2 and 6.0ms-2  respectively? Take the radius of earth as 6400 km:

  • Option 1)

    2600 km

  • Option 2)

    1600 km

  • Option 3)

    1400 km

  • Option 4)

    2000 km

 

Answers (1)

 

Potential due to Uniform solid sphere -

R
ightarrow Radius of sphere

M
ightarrow Mass of sphere

r
ightarrow distance from centre of sphere

Vcentre=frac{3}{2}Vsurface

- wherein

Outside the surface

V=-frac{GM}{r}

on the surface

Vsurface=-frac{GM}{R}

Inside the surface 

r<R

V=-frac{GM}{2R}left[3-left ( frac{r}{R} 
ight )^{2}
ight]

 

 

Gravitational potential at a height h=\frac{-GM}{R+h}.\:.\:.\:.1

 

acceleration due to gravity at the height = h = \frac{GM}{(R+h)^{2}}
                                                                   (g^{1})

or \frac{\left | V \right |}{g^{1}}=R+h

or \frac{5.4\times10^{7}}{6}=6.4\times10^{6}+h

or 0.9\times10^{7}=6.4\times10^{6}+h

or h = 2.6\times10^{6}=2600km 


Option 1)

2600 km

This option is correct.

Option 2)

1600 km

This option is incorrect.

Option 3)

1400 km

This option is incorrect.

Option 4)

2000 km

This option is incorrect.

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