Question

Which of the following is different from the other ?

• A. Period of satellite orbiting around the earth very
  near to its surface
• B. Period of simple pe ndulum of infinite length
• C. Period of moon aroundthe earth
• D. Period of the body dropped in a tunnel bored
  across the earth and through its centre

Answer 1

The correct option is C Period of moon aroundthe earth

$R$ and be the radius of earth.

For A: $T=2\pi \sqrt{\frac{R}{g}}$

For B: $T=2\pi \sqrt{\frac{L}{g}}$

For C: $T=2\pi \sqrt{\frac{r^2\left(r^{\prime }\right)}{g{R}^2}}$

where $r$ and $r^{\prime }$ be the distance of moon from earth and COM of the system respectively

For D : $T=2\pi \sqrt{\frac{R}{g}}$