Multiple choice

A hemispherical vessel of ${ 10 }^{ 3 }$ kg and radius r = 1 m is completely filled with a liquid of mass ${ 2\times 10 }^{ 3 }$ kg The height of center of mass of the system from the ground is

  1. $\dfrac { 7 }{ 12 } m$
  2. $\dfrac { 5 }{ 12 } m$
  3. $\dfrac { 5 }{ 7 } m$
  4. $\dfrac { 4 }{ 9 } m$
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C Correct answer
AI explanation

The center of mass of the hemispherical shell is at r/2 = 0.5 m from the base, while the center of mass of the liquid is at 3r/8 = 0.375 m from the base. Using the formula for combined center of mass, y = (1000 * 0.5 + 2000 * 0.375) / 3000. This calculates to (500 + 750) / 3000, which equals 1250 / 3000. The height of the center of mass of the system is 5/7 m.

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