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Byju's Answer

Standard XII

Physics

Com of Solid Bodies

Consider foll...

Question

Consider following statements. Choose the correct ones:

CM of a uniform semicircular disc of radius R is

2 R π

from the centre.

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CM of a uniform semicircular ring of radius

2 R / 3

4 R / 3 π

from the centre.

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CM of a solid hemisphere of radius R is

4 R / 3 π

from the centre.

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CM of a solid hemisphere shell of radius R is

R / 2

from the centre.

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Solution

The correct options are
B CM of a uniform semicircular ring of radius $2 R / 3$ is $4 R / 3 π$ from the centre.
D CM of a solid hemisphere shell of radius R is $R / 2$ from the centre.
CM of a uniform semicircular disc of radius $R = 4 R / 3$ from the centre
CM of a uniform semicircular ring of radius $2 R / 3 = 2 (2 R / 3) = 4 R / 3$ from the centre
CM of a solid hemisphere of radius $R = 3 R / 8$ from the centre
CM of a hemisphere shell of radius $R = R / 2$ from the centre
So, options B & D are correct.

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Similar questions

Q. Consider the following statements
[1] CM of a uniform semicircular disc of radius

R = 2 R / π

from the centre
[2] CM of a uniform semicircular ring of radius

R = 4 R / 3 π

from the centre
[3] CM of a solid hemisphere of radius

R = 4 R / 3 π

from the centre
[4] CM of a hemisphere shell of radius

R = R / 2

from the centre
Which statement are correct :

Q. In the figure shown, a hole of radius

2 cm

is made in a semicircular disc of radius

6 π

at a distance

8 cm

from the centre

C

of the disc. The distance of the centre of mass of this system from point

C

is: (COM of semicircle of radius

r

is at distance

\frac{4 r}{3 π}

from the base)

Q. In the figure shown, a hole of radius

2 cm

is made in a semicircular disc of radius

6 π

at a distance

8 cm

from the centre

C

of the disc. The distance of the centre of mass of this system from point

C

is: (COM of semicircle of radius

r

is at distance

\frac{4 r}{3 π}

from the base)

Q. The radius of gyration of a solid hemisphere of mass

M

and radius

R

about an axis parallel to the diameter at a distance

\frac{3}{4} R

from this plane is given by (centre of mass of the hemisphere lies at a height

\frac{3 R}{8}

from the base):

Q. A semicircular portion of radius

r = 10 cm

is cut from a uniform rectangular plate as shown in the figure. The distance of center of mass

C

of the remaining plate, from point

O

is (COM of semicircle is at distance

\frac{4 r}{3 π}

from the base)

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