A circular disc of a diameter `'d'` slowly rotated in a liquid of large `'eta'` at a small distance `'h'` from a fixed surface as shown in figure. If an expression for torque `'tau'` necessary to maintain an angular velocity `'omega'` is `(pietad^(4))/(lambdah)` then fidn `lambda`.

A circular disc of a diameter 'd' slowly rotated in a liquid of large viscosity 'eta' at a small distance 'h' from a fixed surface as shown in figure. If an expression for torque 'tau' necessary to maintain an angular velocity 'omega' is (pietad^(4))/(lambdah) then fidn lambda .

A liquid of density rho is in a vessel rotating with angular velocity omega as shown in figure. If P_0 is the atmospheric pressure, find pressure at a radial distance r from the axis. .

A uniform rod of maass m and length L is placed on the fixed cylindrical surface of radius R at an small angular position theta from the vertical (vertical means line joining centre and vertex of the cylindrical path) as shown in the figure and released from rest. Find the angular velocity omega of the rod at the instant when it crosses the horizontal position (Assume that when rod comes at horizontal position its mid point and vertex of the circular surface coincide). Friction is sufficient to prevent any slipping.

Select ALL correct answer : A disc of radius R is placed over a horizontal table in such a way that plane of the disc is horizontal and rotated about its vertical axis passing through its center with angular velocity omega . A layer of grease of thickness l is present between the table and the disc.Coefficient of viscosity of grease is eta .Then, (A) torque needed to rotate the disc with constant angular velocity is (pi eta omega R^(4))/(4l) (B) torque needed to rotate the disc with constant angular velocity is (pi eta omega R^(4))/(2l) (C) power needed to rotate the disc with constant angular velocity is (pi eta omega^(2)R^(4))/(2l) (D) power needed to rotate the disc with constant angular velocity is (pi n omega^(2)R^(4))/(4l)

A disc of mass 4 kg and radius 6 metre is free to rotate in horizontal plane about a vertical fixed axis passing through its centre. There is a smooth groove along the diameter of the disc and two small blocks of masses 2 kg each are placed in it on either side of the centre of the disc as shown in figure. The disc is given initial angular velocity omega_(0) =12 rad/sec and released. Find the angular speed of disc (in radian/sec) when the blocks reach the ends of the disc.

A large rectangular box has been rotated with a constant angular velocity omega_(1) about its axis as shown in the figure. Another small box kept inside the bigger box is rotated in the same sense with angular velocity omega_(2) about its axis (which is fixed to floor of bigger box). A particle P has been identified, its angular velocity about AB would be