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)`
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WORK, ENERGY AND POWER
PHYSICS GALAXY - ASHISH ARORA|Exercise Practice Exercise|42 Videos
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))) .
Two particles, each of mass m are attached to the two ends of a light string of length l which passes through a hole at the centre of a table. One particle describes a circle on the table with angular velocity omega_(1) and the other describes a circle as a conical pendulum with angular velocity omega_(2) below the table as shown in figure -3.86. if l_(1) and l_(2) are the lengths of the portion of the string above and below the table then :
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 attached to the celling of a cabin with an inextensible light string of length l . The cabin is moving upward with an acceleration a . The particle is taken to a position such that string makes an angle theta with vertical. When string becomes vertical, find the tension in the string.
A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that r =L/(sqrt2) . The speed of particle will be :
A particle of mass m is attached to one end of string of length l while the other end is fixed to point h(h lt l) above a 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, is : (l gt h)
A bead of mass m is attached to the mid-point of a taut, weightless string of length l and placed on a frictionless horizontal table. Under a small transverse displacement x, as shown, if the tension in the string is T, then the frequency of oscillation is-
One end of a string is attached to a 6kg mass on a smooth horizontal table. The string passes over the edge of the table and to its other end is attached a light smooth pulley.Over this pulley passes another string to the ends of which are attached masses of 4kg and 2kg respectively. Show that the 6kg mass moves with an acceleration of 8g//17 .
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