From a sphere of radius 1 m, a sphere of radius 0.5 m is removed from the edge. The shift in the C.M. is

# From a sphere of radius 1 m, a sphere of radius 0.5 m is removed from the edge. The shift in the C.M. is

1. A

2. B

3. C

4. D

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### Solution:

Given data:   Sphere with radius 0.5m is removed from the edge of a sphere of radius 1m

Concept Used:  Systems of Particles

Detailed Solution:

As we know,

COM of sphere is located at centre of sphere.

Let mass of sphere of radius 1m be M and its centre be at the origin of a Cartesian system

If a sphere of radius 0.5m is removed from it, COM of small sphere is located at (0.5, 0).

Then, Mass of small sphere $m=\frac{M\left(\frac{4}{3}\mathrm{\pi }{\left(0.5\right)}^{3}\right)}{\left(\frac{4}{3}\mathrm{\pi }{\left(1\right)}^{3}\right)}=M×\left(0.5{\right)}^{3}=\frac{M}{8}$

Now, Centre of mass will be calculated as-

$x=\frac{{m}_{1}{x}_{1}-{m}_{2}{x}_{2}}{{m}_{1}-{m}_{2}}$

m

Similarly, we can find value of y using same formula,

We get, y=0.

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