A particle of mass `m` is attacted to one end of string of length `3L`. The particle is on a smooth horizontal table. The string passes through a hole in the table and to its other end is attached to a small particle of mass `m_(0)`. The particle describe horizontal circular motion with angular velocity `omega_(1)` and `omega_(2)`. find the value of (a) `(omega_(1))/(omega_(2))` and (b) the value of `((1)/(omega_(1)^(2))+(1)/(omega_(2)^(2)))`.

A particle of mass m is attached to one end of a weightless and inextensible string of length L. The particle is on a smooth horizontal table. The string passes through a hole in the table and to its other and is attached a small particle of equal mass m. The system is set in motion with the first particle describing a circle on the table with constant angular velocity omega_(1) and the second particle moving in the horizontal circle as a conical pendulum with constant angular velocity omega_(2) Show that the length of the portions of the string on either side of the hole are in the ratio omega_(2)^(2): omega_(1)^(2)

A particle of mass m is tied to a string of length L and whirled into a horizontal plan. If tension in the string is T then the speed of the particle will be :

A particle of mass m is tied to a string of length L and whirled into a horizontal plan. If tension in the string is T then the speed of the particle will be :

A particle of mass m is attached to one end of a string of length l while the other end is fixed to a point h above the horizontal table. The particle is made to revolve in a circle on the table so as to make p revolutions per second. The maximum value of p if the particle is to be in contact with the table will be :

A particle of mass 'm' is suspended from a ceiling through a string of length'L'. If the particle moves in a horizontal circle of radius 'r', then the speed of the particle is