Question

If a tunnel is cut at any orientation through earth, then in what time will, a ball released from one end, reach the other end (neglect the rotation of the earth) ?

• A. 84.6 minutes
• B. 42.3 minutes
• C. 8 minutes
• D. depends on orientation

Answer 1

Answer: (B)

42.3 minutes

Force and to rque

As we know

g depth = $g(1-\frac{d}{R})$

$g_d=g\left(\frac{R-d}{R}\right)\because (R-d)=x$

$g_d=\frac{g}{R}x$

$F_r=-m{g}_d$

$F_R=\frac{-mgx}{R}\Rightarrow F=-KX$

$T=2\pi \sqrt{\frac{m}{k}}\to$ As we know

$K=\frac{mg}{R}$

$T=2\pi \sqrt{\frac{mR}{mg}}$

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

$T=84.6,minutes$

$A\to B;t=\frac{T}{2}=\frac{84.6}{2}=43.2$