Question

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) 2 $\pi \sqrt{\frac{R}{g}}$
b)$\sqrt{\frac{3\pi }{GD}}$
c)2 $\pi \sqrt{\frac{\pi }{GD}}$
d)2 $\pi \sqrt{\frac{R}{2g}}$

• A. a and b are true
• B. a and c are true
• C. b and c are true
• D. c and d are true

Answer 1

The correct option is A a and b are true

Time period $T=2\pi \sqrt{\frac{l}{g}}$
$T=2\pi \sqrt{\frac{R}{g}}$
but $g=\frac{GM}{R^2}=\frac{G\left(\frac{4}{3}\pi R^3\right)D}{R^2}$
$T=2\pi \sqrt{\frac{R}{GD\frac{4}{3}\pi R}}$
$=\sqrt{\frac{3\pi }{GD}}$