Question

solve this 5th and 6th questions please.............

Answer 1

g = G M /R²
       R = Radius of Earth, M = mass of Earth. G = Gravitational constant. 

g' = acceleration at a height h.
      d = R + h, if the point is above the surface of Earth.

g' = g * R² / d² = g /[ 1 + h/R ]²  ≈ g * [ 1 - 2 h / R ]    if  h << R.

So  g' at h = 64 km above,  = 9.8 * [ 1 - 2 * 64/6400 ] = 9.8* 0.98 m/s²

=======  Below surface of EArth.

 Let  d = distance of point from center of EArth. But d <= R.
         ρ = density of Earth.

  g' = G M' / d²,     where M' = mass of Earth upto radius d only. Don't consider the Earth between radius d and R.  Let d = R - h.

  g' = G * ρ * 4 π/3 * d³ /d²  = G * ρ *4 π d /3
  g = G M / R² = G * ρ * 4 π/3 R³ / R² 

g' = g * d/R = g * [1 - h /R] = 9.8 * (1 - 32/6400) = 9.8 * 0.995 m/s²

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Q6. 
Absolute PE of an object of mass m on the surface of Earth
       = - G M m / R = - m g R  (-ve).

If the KE equals PE in magnitude, then absolute total energy becomes 0. Then the body escapes from the gravitational attraction of Earth.

   So 1/2 m v² = m g R
            v = √[2 g R ] = √[2* 9.81 * 6.370 * 10⁶] = 11.18 km/sec.