A small mass particle is projected with an initial velocity `v_(0)` tangent to the horizontal rim of smooth hemisphereical 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`.

A small particle of mass m is given an initial velocity v_(0) tangent to the horizontal rim of a smooth cone at a radius r_(0) from the vertical slides to point B , a vertical distance h below A and a distance r from the vertical centreline, its velocity v makes an angle theta with the horizontal tangent to the cone through B . The speed of particle at point B

A small particle of mass m is given an initial velocity v_(0) tangent to the horizontal rim of a smooth cone at a radius r_(0) from the vertical slides to point B , a vertical distance h below A and a distance r from the vertical centreline, its velocity v makes an angle theta with the horizontal tangent to the cone through B . The value of theta is

A small particle of mass m is given an initial velocity v_(0) tangent to the horizontal rim of a smooth cone at a radius r_(0) from the vertical slides to point B , a vertical distance h below A and a distance r from the vertical centreline, its velocity v makes an angle theta with the horizontal tangent to the cone through B . The minimum value of v_(0) for which particle will be moving in a horizontal circle of radius r_(0) .

A small particle is given an initial velocity v_(0)=10 m//s along the tangent to the brim of a fixed smooth hemisphere bowl of radius r_(0)=15sqrt(2)m as shown in the figure. The particle slides on the inner surface and reaches point B , a vertical distance h=15m below A and a distance r from the vertical centerline, where its velocity v makes an angle theta with the horizontal tangent to the bowl through B . If theta=15 K^(@) . Find the value of K . (take g=10 m//s^(2) )

The distance of the centre of mass of a hemispherical shell of radius R from its centre is

A particle is projected with velocity v at an angle theta aith horizontal. The average angle velocity of the particle from the point of projection to impact equals

A projectile, thrown with velocity v_(0) at an angle alpha to the horizontal, has a range R. it will strike a vertical wall at a distance R//2 from the point of projection with a speed of