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JIPMER 2014
Exam
JIPMER
Year
2014
Subject
Physics
Chapter
Gravitation

JIPMER 2014 · Physics · Gravitation

Change in acceleration due to gravity is same upto a height h from...

Change in acceleration due to gravity is same upto a height hh from each other the earth surface and below depth xx, then relation between xx and hh is ( hh and x<<<Rex\lt\lt \lt R_e )

Options

  1. Ax=hx=h
  2. Bx=2hx=2 h
  3. Cx=h2x=\frac{h}{2}
  4. Dx=h2x=h^2

Correct answer

B. x=2hx=2 h

Step-by-step solution

Variation in gg at a height hh from the earth surface g′=g(1−2hRe)g^{\prime}=g\left(1-\frac{2 h}{R_e}\right) Variation in gg at a depth xx below the earth surface g′′=g(1−xRb)g^{\prime \prime}=g\left(1-\frac{x}{R_b}\right) But variations are same ∴g(1−2hRθ)=g(1−xRθ)\therefore \quad g\left(1-\frac{2 h}{R_\theta}\right)=g\left(1-\frac{x}{R_\theta}\right)\therefore \quad x=2 h
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