Question

show that the total energy is conserved if the ball of mass M is thrown downwards from a height h

Answer 1

Reffer to isce physics class 10 diagram.They are very clear and easily understood.

Answer 2

first of all you need to know than  energy  can neither be created nor be destroyed

total mechanical energy is conserved  for   for work done by every conservative force  

since , gravity is a conservative force ( you will study in class 11 ) so mechanical energy is also conserved when work is done by gravity  or you can say when a ball of mass is thrown under the influence of gravity      

you can see in  image   also  

 CASE 1

when ball is at max height at rest    PE = mgh   and  KE  = 0 as velocity of ball is zero         total mechanical energy is     mgh

CASE 2  

when ball is  in free fall  and  ascends through height  h1  where maximum height is h now   PE =mg(h-h1)  and  since mechanical energy is conserved  the   PE get transformed into  KE     and   KE=mgh1  now total mecchanical energy is KE + PE =mgh

CASE 3

when ball  strikes ground  PE due to  height  becomes zero  since  energy is conserved    the PE  gets transformed to KE  =mgh    total mechanical energy is mgh as PE is zero  as height is zero  

THEREFORE  TOTAL ENERGY IS CONSERVED