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AIIMS 2012
Exam
AIIMS
Year
2012
Subject
Physics
Chapter
Gravitation

AIIMS 2012 · Physics · Gravitation

Find out the correct relation for the dependance of change in...

Find out the correct relation for the dependance of change in acceleration due to gravity on the angle at the latitude, due to rotation of earth

Options

  1. Adg∝cos⁡ϕd g \propto \cos \phi
  2. Bdg∝cos⁡2ϕd g \propto \cos ^2 \phi
  3. Cdg∝cos⁡3/2ϕd g \propto \cos ^{3 / 2} \phi
  4. Ddg∝1cos⁡ϕd g \propto \frac{1}{\cos \phi}

Correct answer

B. dg∝cos⁡2ϕd g \propto \cos ^2 \phi

Step-by-step solution

Effective acceleration due to gravity due to rotation earth is given as g′=g−Rω2cos⁡2ϕ∴ Change in acceleration, dg=Rω2cos⁡2ϕ∴dg∝cos⁡2ϕ\begin{aligned} & g^{\prime}=g-R \omega^2 \cos ^2 \phi \\ \therefore & \text{ Change in acceleration, } d g=R \omega^2 \cos ^2 \phi \\ \therefore & d g \propto \cos ^2 \phi\end{aligned}
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