I don't think it's the center of mass that's important in this problem. It's the moments about the point that the block will pivot, i.e. point D.
Have you computed those moments?
where k is the density of that material
mass of cuboid 50*10*10k distance from x-axis= 5
mass of other cuboid 10*10*10k distance from x-axis=15
mass of cylinder pi*4*4*40k distance from x-axis=15
mass of cylinder pi*4*4*40k distance from x-axis=15
total mass (6000+1280pi)k distance from x-axis 10
according to me it should not topple but the book says it will topple and then when we replace these handles with 39.5 ones it wont topple
How did you deterimine the distance from x axis = 10? To find the CG youo add up all the masses times the distance of their CG from some datum (x -axis as you called it, which I assume is the line BC - is fine), and then divide by the total mass:
(5000x5 + 1000x15 + 1280 pi x 15)/(5000+1000+1280 pi)
You'll find this gives a value that is larger than 10, so the CG is to the left of D.
bro i did the same thing i got 10.0106 that is approximately 10 which means it is on the point of toppling but it does not topple
and even when we reduce the cylinders to 39.5 i get
(5000*5)+(1264pi*15)+(1000*15)/(6000+1264pi)=9.985444306 again 10 i dont know what is wrong
But 10.01 is greater than 10 (just barely), so it topples. It seems whoever wrote this problem ignored the issue of how many significant digits are needed in the dimensions.
Nothing wrong, except your conclusion. 9.98 is less then 10, so it stays upright.
One of the things I really don't like about how this problem is presented is that the dimensions are given to only 2 significant digits, so actually rounding these answers to 10 and saying it's inconclusive is a better answer than stating whether it topples or not. The dimensions provided need to be accyrate to at least 4 digits of accuracy in order to be sure. So instead of giving dimensions like "10 cm" the drawing should haveit as "10.00 cm."