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Gravitation question

2016 · Q140
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Gravitation question

2016 · Q140

NEETPhysicsGravitationMCQ+4 / −1
At what height from the surface of earth the gravitation potential and the value of g are −-−5.4 ×\times× 107 J kg−-−1 and 6.0 m s−-−2 respectively? Take the radius of earth as 6400 km.
  1. A
    1400 km
  2. B
    2000 km
  3. C
    2600 km
  4. D
    1600 km
View written solutionFree

Correct answer: C

As we know, gravitational potential (v) and acceleration due to gravity (g) with height

V=−GMR+h=−5.4×107V = {{ - GM} \over {R + h}} = - 5.4 \times {10^7}V=R+h−GM​=−5.4×107   ...(i)

and g=GM(R+h)2=6g = {{GM} \over {{{\left( {R + h} \right)}^2}}} = 6g=(R+h)2GM​=6   ...(ii)

Dividing (i) by (ii)

−GMR+hGM(R+h)2=−5.4×1076{{{{ - GM} \over {R + h}}} \over {{{GM} \over {{{\left( {R + h} \right)}^2}}}}} = {{ - 5.4 \times {{10}^7}} \over 6}(R+h)2GM​R+h−GM​​=6−5.4×107​

⇒−5.4×107(R+h)=6 \Rightarrow {{ - 5.4 \times {{10}^7}} \over {\left( {R + h} \right)}} = 6⇒(R+h)−5.4×107​=6

⇒\Rightarrow⇒ R + h = 9000 km so, h = 2600 km

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