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Suppose a smooth tunnel is dug along a s...

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 the earth is uniformly distributed over its volume. Then, which of the following statements are not correct?

A

(a)The partical will emerge from the other end with velocity `sqrt((GM_(e))/(2R_(e)))` where `M_(e)` and `R_(e)` are earth's mass and radius respectively

B

(b)The particle will come to rest at centre of the tunnel because at this position, particle is closest to earth centre.

C

(c)Potential energy of the particle will be equal to zero at centre of tunnel if it is along tunnel's diameter.

D

(d)Acceleration of the particle will be proportional to its distance from midpoint of the tunnel.

Text Solution

Verified by Experts

The correct Answer is:
D
Acceleration of the particle from the centre of the earth is directly proportional to the distance from the centre
`impliesa=(GMx)/(R^(3))impliesapropx impliesa=-omega^(2)x`
Particle will perform oscillatory motion.
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