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Question

A solid cone of height 2R and base radius R is placed over a solid hemisphere as shown in figure. Cone and hemisphere are made up of the same material. Height of center of mass of system from the ground is

  1. 58R
  2. 32R
  3. 1716R
  4. R


Solution

The correct option is C 1716R
Mass of hemispherical part, m1=ρ23πR3   Mass of conical part, m2=ρ13πR2×2R=ρ23πR3   Thus, m1=m2=mHeight of centre of mass of hemispherical part from ground, y1=58RHeight of centre of mass of conical part from ground, y2=R+R2=32RCentre of mass of whole body, ycom=m1y1+m1y1m1+m2ycom=58R+32R2=1716R

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