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Q.

A tunnel is dug along the diameter of the earth. There is a particle of mass m at the centre of the tunnel. Find the minimum velocity given to the particle so that is just reaches to the surface of the earth. $(R = radius of earth)$

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a

\sqrt{\frac{GM}{R}}

b

\sqrt{\frac{GM}{2R}}

c

It will reach with the help of negligible velocity

d

\sqrt{\frac{2GM}{R}}

answer is A.

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Detailed Solution

v_{0} = \sqrt{\frac{GM}{R}}

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A tunnel is dug along the diameter of the earth. There is a particle of mass m at the centre of the tunnel. Find the minimum velocity given to the particle so that is just reaches to the surface of the earth. (R=radius of earth)