Question

What can be said about the centre of mass of a uniform hemisphere without making any calculation? Will its distance from the centre be more than r/2 or less than r/2?

Answer 1

Answer:

its at distance of 3r/8 from its base...most probably

Answer 2

Explanation:

• Let us consider a uniform cylinder with radius r and height r. From the centre of the base circle, the centre of mass of a uniform hemisphere will be at distance $\frac{r}{2}$ and the distance of the uniform hemisphere from the centre will be less than $\frac{r}{2}$.  
• By carving out masses from the upper parts of the uniform cylinder the given hemisphere can be formed.  
• This shows that the centre of mass of the remaining part of the hemisphere will be less than $\frac{r}{2}$.