A particle rotates in a horizontal circle of radius 'R' in a conical funnel with constant speed 'V'. The inner surface of the funnel is smooth. The height of the plane of the circle from the vertex of the funnel is (g-acceleration due to gravity)

For a particle in uniform circular motion

A disc at rest is subjected to a uniform angular acceleration about its axis. Let $\theta$ and $\theta_1$ be the angle made by the disc in $2^{\text {nd }}$ and $3^{\text {rd }}$ second of its motion. The ratio $\frac{\theta}{\theta_1}$ is

A body moves along a circular path of radius 15 cm . It starts from a point on the circular path and reaches the end of diameter in 3 second, The angular speed of the body in $\mathrm{rad} / \mathrm{s}$ is