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A wire is bent an an angle theta. A rod ...


A wire is bent an an angle `theta`. A rod of mass m can slide along the bended wire without friction as shown in Fig. A soap film is maintained in the frame kept in a vertical position and the rod is in equilibrium as shown in the figure. If rod is displaced slightly in vertical direction, then the time period of small oscillation of the rod is

Text Solution

Verified by Experts

The correct Answer is:
`2 pi sqrt((l)/(g))`

`2T(2l "tan"(theta)/(2))=mg`
If x be the displacement in vertical direction of the rod from equilibrium position
`F_("res")=-2x "tan"(theta)/(2) T xx2,a =(-4T "tan"(theta)/(2))/(m)x`
`T=2pi sqrt((m)/(4T "tan"(theta)/(2)))=2 pi sqrt((m)/(4(mg)/(4l)))=2pi sqrt((l)/(g))`
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