GravitationHard
Question
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
Options
A.The particle will emerge from the other end with velocity 
where Me and Re are Earth′s mass and radius respectively
where Me and Re are Earth′s mass and radius respectivelyB.The particle will come to rest at centre of the tunnel because at this position, particle is closest to Earth centre.
C.Potential energy of the particle will be equal to zero at centre of tunnel if it is along tunnel′s diameter
D.Acceleration of the particle will be proportional to its distance from midpoint of the tunnel
Solution
Acceleration of the particle from the centre of the earth is directly proportional to the distance from the centre
⇒ a =
⇒ a ∝ x ⇒ a = ω2x
Particle will perform oscillatory motion.
⇒ a =
⇒ a ∝ x ⇒ a = ω2xParticle will perform oscillatory motion.
Create a free account to view solution
View Solution FreeMore Gravitation Questions
A planet is revolving around the Sun in an elliptical orbit. Its closest distance from the Sun is rmin. The farthest dis...The rotation of the Earth having radius R about its axis speeds upto a value such that a man at latitude angle 60o feels...Which of the following statements is true for the planets orbiting around the sun ?...A double star is a system of two stars of masses m and 2m, rotating about their centre of mass only under their mutual g...The height at which the acceleration due to gravity becomes (where g = the acceleration due to gravity on the surface of...