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A frictionless tunnel is dug along a chord of the earth of at a perpendicular distance R/2 from the centre of earth (where R is radius of earth). An object is released from one end of the tunnel.

The correct graph, showing the variation of magnitude of acceleration of object with its distance from centre of earth is

The correct answer is:


    Force due to gravitational field at a distance r, in radial direction.

    F equals fraction numerator 4 pi over denominator 3 end fraction G rho r m
    Component of force along AB
    table attributes columnalign left end attributes row cell equals F cos theta equals fraction numerator 4 pi over denominator 3 end fraction G m fraction numerator M subscript e over denominator 4 over 3 pi R cubed end fraction r fraction numerator square root of r squared minus R squared over 4 end root over denominator r end fraction end cell row cell F subscript A B end subscript superscript apostrophe equals m fraction numerator G M subscript e over denominator R cubed end fraction square root of r squared minus open parentheses R squared over 4 close parentheses end root end cell row cell a subscript A B end subscript equals fraction numerator G M subscript e over denominator R cubed end fraction square root of r squared minus open parentheses R squared over 4 close parentheses end root end cell end table

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