from the base of a hemisphere,a right cone of height R/2 and same base has been scooped out. Find the Centre of Mass...ans-11R/24

Center of Mass of uniform right cone is h/4 from its base where h is its height .Center of Mass of Hemisphere is 3r/8 from its base as shown :In this case h = r/2 , so h/4 = r/8we can assume uniform density and use the concept of negative mass . From symmetry we know that center of mass must lie on the y axis .Volume of Hemisphere = (π.r3).2/3(π.r3).2/3Volume of cone =(π.r2.r/2)/3=(π.r3).(1/6)(π.r2.r/2)/3=(π.r3).(1/6)Center of mass =(2/3∗3r/8–1/6∗r/8)/(2/3–1/6)=(11/24)r