Question

If a hemisphere of same radii is mounted on a solid cylinder then what will be the formula for area of sheet required to cover it ??
Please give correct answers​

Answer 1

Answer:

Let the point O be the origin.

Mass of cylinder = πR

2

Hρ with center of mass (0,

2

−H

)

Mass of hemisphere = M

h

=

3

2πR

3

ρ

Center of mass of hemisphere calculation

Consider a disc of thickness dy at height y from O

radius of this disc will be given by r

2

=R

2

−y

2

y co-ordinate of center of mass =

M

h

1

∫

0

R

yπ(R

2

−y

2

)ρ∂y

=

M

h

1

[

4

πρR

4

]

=

8

3R

So co-ordinate of center of mass of hemisphere = (0,

8

3R

)

As effective center of mass = (0,0)

For the COM of the system to be at O, m

1

×OS=M

2

×OC

=>πR

2

Hρ∗

2

H

=

3

2πR

3

ρ

∗

8

3R

=> H=

2

R

=

2

2

2

m

=2m

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