Question

a disc of radius r is removed from the disc of radius R then
a)the minimum shift in centre of mass is zero
b)maximum shift in centre of mass cannot be greater than r2/R+r
c)centre of mass must lie where centre of mass exist
the shift in centre of mass is r2/R+r​

Answer 1

Answer:

hi

Explanation:

Let the circular disc be placed in the x−y plane.

Let the center of the complete disc of radius 2R be at origin and the center of the removed disc be on x=R. Let the mass of complete disc be M.

Then, position vector of center of mass of smaller disc is

x

1

=R

i

^

.

Let the center of mass of the new disc be at (x,y). Then, its position vector is given by

x

2

=x

i

^

+y

j

^

Mass of disc is proportional to its area.

M

M

1

=

A

A

1

=

π4R

2

πR

2

=

4

1

Mass of new disc is given by M

2

=M−M

1

=

4

3

M

Now, position vector of center of mass of complete disc is given by the formula,

x

cm

=

M

1

+M

2

M

1

x

1

+M

2

x

2

∴0=

M

4

M

R

i

^

+

4

3M

(x

i

^

+y

j

^

)

Equating the co-efficients of

i

^

and

j

^

from both sides, we get:

x=−

3

R

,y=0

Distance from center of big disc, d=

3

R

=αR, given.

So, α=

3

1

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