A hoop of radius r and mass m rotating with an angular velocity ω0 is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?
The circle passing through (1, -2) and touching the axis of x at (3, 0) also passes through the point
Match List - I (Fundamental Experiment) with List - II (its conclusion) and select the correct option from the choice given below the list :
Let a,band c be three non-zero vectors such that no two of them are collinear and (a×b)×c=31∣c∣∣∣b∣∣∣a∣. If θis the angle between vectors band cthen a value of sinθis :
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of the gas is V0 and its pressure is P0. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency:
The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1), (1, 1) and (1, 0) is