Two small rings O and O' are put on two vertical stationary rods AB and A'B', respectively. One end of an inextensible thread is tied at point A'. The thread passes through ring `O'` and its other end is tied to ring O. Assuming that ring O' moves downwards at a constant velocity `v_(1)`, then velocity `v_(2)` of the ring O, when `/_AOO'=alpha` is

Two small rings O and O' are put on two vertical stationery rods AB and A'B' , respectively. One end of an inextensible thread is tied at point A' . The thread passes through ring O' and its other end is tied to ring O . Assuming that ring O' moves downwards at a constant velocity v_(1) , determine the velocity v_(2) of the ring O , when /_AOO'=alpha .

Two rings O and O' are put on two vertical stationary rods AB and A'B' respectively as shown in figure. An inextensible string is fixed at point A' and on ring O and is passed through O' moves downwards at a constant speed v, find the velocity of the ring O in terms of alpha .

A ring A which can slide on a smooth wire is connected to one end of a string as shown in fig. Other end of the string is connected to a hanging mass B. Find the speed of the ring when the string makes an angle theta with the wire and mass B is going down with a velocity v.

The moment of inertia of a uniform rod about a perpendicular axis passing through one end is I_(1) . The same rod is bent into a ring and its moment of inertia about a diameter is I_(2) . Then I_(1)//I_(2) is

A small bead of mass m moving with velocity v gets threaded on a stationary semicircular ring of mass m and radius R kept on a horizontal table. The ring can freely rotate about its centre. The bead comes to rest relative to the ring. What will be the final angular velocity of the system?

A uniform conducting wire is used to make a ring and its two diameters AB and CD. The ring is placed in a uniform magnetic field B perpendicular to its plane. The resistance of the wire per unit length is lambda Omega//m . (a) Find the current in BO and BC when the ring is moved with constant velocity v in its plane. (b) Find current in BO and BC when the ring is kept stationary but the magnetic field is increased at a constant rate of (dB)/(Dt) = alpha T//s . Assume that magnetic field is confined inside the circular ring only. Take radius of the ring to be a.

A particle is moving in a straight line and passes through a point O with a velocity of 6ms^(-1) The particle moves with a constant retardation of 2ms^(-2) for 4 s and there after moves with constant velocity. How long after leaving O does the particle return to O

A particle of mass 5kg is free to slide on a smooth ring of radius r=20cm fixed in a vertical plane. The particle is attached to one end of a spring whose other end is fixed to the top point O of the ring. Initially, the particle is at rest at a point A of the ring such that /_OCA=60^@ , C being the centre of the ring. The natural length of the spring is also equal to r=20cm . After the particle is released and slides down the ring, the contact force between the particle and the ring becomes zero when it reaches the lowest position B. Determine the force constant (i n xx 10^2Nm^-1) of the spring.