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When a hole is drilled along the diameter of the earth and if a body is dropped into it, it executes SHM with a period T equal to (R&D are radius and density of the earth)

a) $\large 2\pi \sqrt {\frac{R}{g}}$ $\large b)\,\,\sqrt {\frac{{3\pi }}{{GD}}}$

$\large c)\,\,2\pi \sqrt {\frac{\pi }{{GD}}}$ $\large d)\,\,2\pi \sqrt {\frac{R}{{2g}}}$

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a and b are true

c and d correct

a and c are true

b and c are true

answer is A.

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Detailed Solution

At a radial distance r,

$\frac{d^{2} r}{d t^{2}} = - \{\frac{4}{3} π G D\} r$

This equation represents SHM. whose time period is

Also, at a radial distance,

The above equation represents SHM whose time period is

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