1.

A small sized mass `m` is attached by a massless string (of length `L`) to the top of a fixed frictionless solid cone whose axis is vertical. The half angle at the vertex of cone is theta. If the mass `m` moves around in a horizontal circle at speed `v` , what is the maximum value of `v` for which mass stay in contact with the comes? (g is acceleration due to gravity.) A. `sqrt(gLcostheta)`B. `sqrt(gLsintheta)`C. `sqrt(gLsinthetatantheta)`D. `sqrt(gl tantheta)`

Answer» Correct Answer - C
At maximum velocity the mass will just loose contact with cone and will behave like free conical pendulum with time period
`T=2pisqrt((Lcostheta)/(g))` implies `omega=(2pi)/(T)sqrt((g)(Lcostheta))`
Hence `v_(max)=(Lsintheta)omega=sqrt(gLsinthetatantheta)`


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