11) A particle of mass 5 × 10 - 5   kg is placed at the lowest point of a smooth parabola x2 = 40y. If it is displaced slightly such that it is constrained to move along the parabola, the angular frequency of oscillation will be :-



(A) g 5                 (B) g 20                 (C) g 10                 (D) None

Dear student

The given equation of parabola is ​X2=40y.
So the potential is given by V==mgy=mg40x2 and if the particle is slightly displaced from its centre then it will oscillate about the centre and the angular frequency is given by 
ω=1md2Vdx2
dVdx=mg20xd2Vdx2=mg20thus ω=1mmg20ω=g20
So correct option is (B).

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