- Home
- Standard 11
- Physics
7.Gravitation
normal
If a tunnel is cut at any orientation through earth, then a ball released from one end will reach the other end in time ........ $\min$ (neglect earth rotation)
A
$84.6$
B
$42.3$
C
$8$
D
depends on orientation
Solution
$g_{d}=g\left(1-\frac{d}{R}\right)$
$g_{d}=\frac{g}{R} x$
$F_{R}=-m g_{d} \Rightarrow F_{R}=-\frac{m g}{R} x$
$T=2 \pi \sqrt{\frac{m R}{m g}} \Rightarrow T=2 \pi \sqrt{\frac{R}{g}}$
$T=84.6 \mathrm{min}$
$t=\frac{T}{2} \Rightarrow t=42.3 \mathrm{min}$
Standard 11
Physics
