Question

find the centre of mass of three particles at the vertices of an equilateral triangle.the masses of the particles are 100g,150g and 200 g respectively.each side of the equilateral triangle is 0.5m long.​

Answer 1

Answer:

Explanation:

Given, Radius=R,Height=  

2

R

​  

 

So, CM of the uniform right-cone is  

4

h

​  

 from its base where h is its height. CM of the hemisphere is  

8

3R

​  

 from its base,

Since,  h=  

2

R

​  

=  

4

h

​  

=  

8

R

​  

 

Bu assuming uniform density and use the concept the negative mass from symmetry we know that CM must lie in the y_axis. Volume of hemisphere =  

3

π

​  

×  

3

2

​  

(πR  

3

)  

3

2

​  

× Volume of cone,

=  

3

πR  

2

 

2

R

​  

 

​  

=  

6

πR  

3

 

​  

 

Therefore the CM=  

3

2

​  

−  

6

1

​  

 

3

2

​  

×  

8

3R

​  

−  

6

1

​  

×  

8

R

​  

 

​  

=  

24

11

​  

R