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GRAVITATION
     
    In these questions, where necessary, use the following:
    G=6.10-11Nm2kg-2
    mass of earth M=6.1024kg
    radius of earth R=6400km
     
1.   Calculate the magnitude of the earth’s gravitational field strength at a point 1500km above the surface of the earth.
     
2.   Calculate the gravitational potential at a point on the earth’s surface.
     
3. The acceleration due to gravity at the surface of the moon is about 1.6ms-2.
    The diameter of the moon is about 3460km.
    Use these figures to calculate the average density of the moon.
     
4.   A space-ship is moving directly away from the earth.
    When it is just outside the earth’s atmosphere, it is moving at 5kms-1.
    If the rocket motors are stopped at this point, how far away from the centre of the earth will the space-ship be when it starts to "fall" back towards the earth
    N.B. the height of the earth’s atmosphere is very small compared with the radius of the earth.
     
5.   Assume the earth to be a sphere of uniformly distributed mass.
    Let g1 be the gravitational field strength at a point 2000km above the earth’s surface and let g2 be the gravitational field strength at a point 2000km below the earth’s surface.
    Calculate the ratio g1/g2.
     
6.   A person can jump (vertically) 2.5m on the earth.
    How high could the same person jump on a planet which has twice the average density of the earth and three times the radius of the earth?
     
7.   A planet has half the radius of the earth and the acceleration due to gravity on the planet is found to be twice the acceleration due to gravity on the earth.
    If the average density of the earth is ρ, calculate the average density of the other planet (in terms of ρ).
     
8.   A planet of mass m1=6×1024kg has a satellite (moon) of mass m2=4×1023kg orbiting at a distance r=3×105km.
    Calculate
  a) the value of g at 104km from the centre of the planet
  b) the distance from the centre of the planet at which g=zero.
 
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