Alternative solution:
If we let θ to be the angle which the bug made with the vetical when it lost contact with the surface. Then the Work done by the weight of the bug will be:
Q.E.D
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The centripetal force on the bug is given by
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When contact with the surface is lost, R = 0; then
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At that point the potential energy lost by dropping the vertical height is equal to the kinetic energy gained:
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[1] & [2] ⇒
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Note: this problem ought to be solved by physicists or mathematicians with sufficient ground in physics (if you are not, don't try it...?). I have more then one solution.
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