A bead of mass m can slide on a frictionless wire as shown in figure. Because of the given shape of the wire, near P, the bottom point, it can be approximated as parabola. Near P, the potential energy of the bead is given U = cx2 where c is a constant and x is measured from P. The bead, if displaced slightly from point P will oscillate about P. The period of oscillation is
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a
2πcm
b
2πm2c
c
2πmc
d
2π2cm
answer is B.
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Detailed Solution
U = Cx2 F = -dUdx ⇒ ma = - 2cx ⇒a =-2cmx⇒ω = 2cm ⇒ T = 2πω = 2πm2c