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Center of Mass as an Average Point

Where is the ...

Question

Where is the Center of Mass of the 3 particle system shown in above figure?

A

X_{c m} = 1.15 Y_{c m} = 1.5

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B

X_{c m} = 1.07 Y_{c m} = 1.33

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C

X_{c m} = 1.5 Y_{c m} = 1.6

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D

None of these

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Solution

The correct option is B $X_{c m} = 1.07 Y_{c m} = 1.33$

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The sphere shown in figure lies on a rough plane when a particle of mass 'm' traveling at a speed $v_{0}$ collides and sticks with it. If the line of motion of the particle is at a distance h above the plane, find the angular speed of the combined system just after the collision. Assume that the mass M of the sphere is large compared to the mass of the particle so that the center of mass of the combined system is not appreciably shifted from the center of the sphere.

The sphere shown in figure lies on a rough plane when a particle of mass 'm' traveling at a speed $v_{0}$ collides and sticks with it. If the line of motion of the particle is at a distance h above the plane, find the angular speed of the combined system just after the collision. Assume that the mass M of the sphere is large compared to the mass of the particle so that the center of mass of the combined system is not appreciably shifted from the center of the sphere.

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