You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

COM of Center of Masses

A semicircula...

Question

A semicircular ring of mass $m$ and a semicircular disc of mass $2 m$ of same radius are joined together as shown. Find the distance of COM from their geometric centre.

\frac{2 R}{3 π}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{2 R}{9 π}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{5 R}{3 π}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{2 R}{9 π}$
Let their geometric centre be at origin.
COM of semicircular disc, $y_{1} = \frac{4 R}{3 π}$
COM of semicircular ring, $y_{2} = \frac{- 2 R}{π}$
So, COM of the combined body $= \frac{m_{1} y_{1} + m_{2} y_{2}}{m_{1} + m_{2}}$
$= \frac{(2 m) \frac{4 R}{3 π} + m \frac{(- 2 R)}{π}}{m + 2 m}$
$= \frac{2 R}{9 π}$

Suggest Corrections

Similar questions

Q. A semicircular ring of mass

m

and a semicircular disc of mass

2 m

of same radius are joined together as shown. Find the distance of COM from their geometric centre.

Q. Two semicircular rings of linear mass densities

λ

and

2 λ

and of radius

3 π cm

each, are joined together to form a complete ring as shown in the figure given below.

Then, distance of the center of the mass of the complete ring from its centre will be:

Q. Two semicircular rings of linear mass densities

λ

and

2 λ

and of radius

3 π cm

each, are joined together to form a complete ring as shown in the figure given below.

Then, distance of the center of the mass of the complete ring from its centre will be:

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)

Join BYJU'S Learning Program

A semicircular ring of mass m and a semicircular disc of mass 2m of same radius are joined together as shown. Find the distance of COM from their geometric centre.

The correct option is B 2R9πLet their geometric centre be at origin. COM of semicircular disc, y1=4R3π COM of semicircular ring, y2=−2Rπ So, COM of the combined body =m1y1+m2y2m1+m2 =(2m)4R3π+m(−2R)πm+2m =2R9π

A semicircular ring of mass $m$ and a semicircular disc of mass $2 m$ of same radius are joined together as shown. Find the distance of COM from their geometric centre.