A straight tunnel is dug into the Earth as shown in the figure at a distance from its center. A ball of mass is dropped from one of its ends. The time it takes to reach the other end is approximately equal to
Step 1: Given information
Consider the figure given below
Step 2: Calculations required
The gravitational force on mass at distance is,
Where, is the gravitational constant, is the mass of the Earth, is the radius of the Earth, and is the distance from the center O.
From the figure given below,
Now,
Since , its motion is simple harmonic in nature. Further,
Hence the time period of oscillation is,
Where, is the time period.
The time take for a particle to go from one end to another is,
Therefore, option (A) is correct.