A particle at angular position `theta_(0)` inside a fixed smooth hemispherical bowl of radius r is projected horizontally with velocity `v_(0)`. Calculate its value so that the particle may rise to the top.

A particle rests on the top of a smooth hemisphere of radius r . It is imparted a horizontal velocity of sqrt(etagr) . Find the angle made by the radius vector joining the particle with the vertical at the instant the particle losses contact with the sphere.

A small particle is placed at the top point A of a fixed smooth hemisphere of radius R. Particle is given small displacement towards right and it starts slipping. Calculate velocity of the particle after hitting horizontal perfectly inelastic surface.

A particle of mass m is released from the top of a smooth hemisphere of radius R with the horizontal speed mu . Calculate the angle with verticle where it loses contact with the hemisphere.

A particle of mass m initially at rest starts moving from point A on the surface of a fixed smooth hemisphere of radius r as shown. The particle looses its contact with hemisphere at point B.C is centre of the hemisphere. The equation relating theta and theta' is .

A horizontal plane supports a fixed vertical cylinder of radius R and a particle is attached to the cylinder by a horizontal thread AB as shown in Fig. The particle initially rest on a horizontal plane. A horizontal velocity v_(0) is imparted to the particle, normal to the threading during subsequent motion. Point out the false statements:

A small block of mass m is released from rest from position A inside a smooth hemispherical bowl of radius R as shown in figure Choose the wrong option.

A particle moving on the inside of a smooth sphere of radius r describing a horizontal circle at a distance r//2 below the centre of the sphere. What is its speed ?

A particle is given an intial soeed u inside a smooth spherical shell of radius R so that it is justable to compelte the circle. Acceleration of the particle, when its velocity is vertical, is

When a particle is projected from the surface of earth its mechanical energy and angular momentum about center of earth at all time are constant. Q. A particle of mass m is projected from the surface of earth with velocity v_(0) at angle 0 with horizontal suppose h be the maximum height of particle from surface of earth and v its speed at that point then v is v_(0)cos0

A small mass particle is projected with an initial velocity v_(0) tangent to the horizontal rim of smooth hemisphereicla bowl at a radius r_(0) from the vertical centre line, as shown at point A. As the particle slide past point B , a distance h below A and distance r from the verticle centre line, its velocity v makes an angle theta with the horizontal tangent to the bowl through B . Determine theta .