Question

A, B, C and D are four point on a hemispherical cup placed inverted on the ground. Diameter BC = 50 cm. A 250 g particle at rest at A, slide down along the smooth surface of the cup. Calculate it’s (a) Potential energy at A relative to B.(b) Speed at the point B (Lowest point).(c) Kinetic and potential energy at D.

Answer 1

The altitude of point A (top point of hemispherical cup) : relative to B.
    = radius = 25 cm
PE =  m g h = 0.250 kg * 10 m/sec^2 * 0.25m = 0.625 J

speed at B:  v m/s
  KE at B = PE at A   --- energy conservation.
  1/2 m v^2 = 0.625 J
   v = 5 √2 m/s 

It is not clear where the point D is ....
If we know the height at point D, then we can calculate PE and then find the KE by  0.625 J - PE.