Question

A solid circular cone of radius R is joined to a uniform solid hemisphere of radius R. Both are made of same material. The center of mass of composite solid lies at the common base. Find the height​

Answer 1

Answer:

ANSWER

REF.Image.

Volume of cone =

3

1

πr

3

h

Mass of cone, m

1

=p×

3

1

πr

2

h

Mass of hemisphere, m

2

=p×

2

1

×

3

4

πr

3

=p×

3

2

πr

3

Now, Y=

m

1

+m

2

m

1

y

1

+m

2

y

2

0=

p×

3

1

πr

2

h+p×

3

2

πr

3

p×

3

1

πr

2

h×

4

h

+p×

3

2

πr

3

(−

8

3r

)

or p×

3

1

πr

2

[

4

h

2

−2r×

8

3r

]=0

or

4

h

2

−

4

3r

2

=0 or h=

3

r