Question with Solution
Suppose a smooth tunnel is dug along a straight line joining two points on the surface of the earth and a particle is dropped from rest at its one end. Assume that mass of earth is uniformly distributed over its Volume. Then [3]
Options:
Answer:
Solution:
Inside a uniform earth the field grows linearly with distance from the centre, and its component along the tunnel points toward the tunnel's midpoint with magnitude proportional to the distance from the midpoint. The particle therefore executes SHM in the tunnel: acceleration proportional to distance from the midpoint - (D) correct.
(A) is wrong: by energy symmetry it reaches the other end with zero speed. (B) is wrong: its speed is maximum at the midpoint. (C) is wrong: the potential energy at the centre is not zero.
Ans (D)
