Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (R/2) from the earth’s centre, where ‘R’ is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period

Correct Option - 1


Detailed Solution:

F = m E cos θ

$$ $=m\left(\frac{GM}{R^3}\times r\right)\times \frac{x}{r}$ $ma=\frac{mg}{R}\times \Rightarrow a=\frac{g}{R}x$

$\Rightarrow T=2\pi \sqrt[]{\frac{R}{g}}$

 

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