
Two bodies of mass and have position vectors and respectively. The centre of mass of this system has a position vector:
(A)
(B)
(C)
(D)
Answer
419.4k+ views
Hint: In order to answer this question, we need to understand that the centre of mass of the system of particles is defined as the position where all the mass of the system of particles is considered to be. It is the point where if linear force is applied on the system, then there will not be any angular acceleration.
Formula Used:
The formula of the centre of mass is given by,
Where centre of mass is and mass of different particles are and the different vector positions are
Complete answer:
It is given in the problem that Two bodies of mass and are placed at position vector and respectively and we need to find the position of the centre of mass of the particles.
The mass of two bodies is also the position vector of the two bodies is and
The formula of the centre of mass is given by,
Where centre of mass is and mass of different particles are and the different vector positions are
Replacing the mass and the position vector in the above formula we get,
Now substitute the values,
Rearrange the terms for further calculations,
Now, divide it be 4 we get
So, the centre of mass of the system of particles is equal to
Hence the correct option is (C).
Note:
The students are advised to understand and remember the formula of the centre of mass as it is very useful in solving problems like this. The centre of mass can be present outside the physical bodies. The centre of mass is an inertial frame and it is at rest compared to the origin of the coordinate system.
Formula Used:
The formula of the centre of mass is given by,
Where centre of mass is
Complete answer:
It is given in the problem that Two bodies of mass
The mass of two bodies is
The formula of the centre of mass is given by,
Where centre of mass is
Replacing the mass and the position vector in the above formula we get,
Now substitute the values,
Rearrange the terms for further calculations,
Now, divide it be 4 we get
So, the centre of mass of the system of particles is equal to
Hence the correct option is (C).
Note:
The students are advised to understand and remember the formula of the centre of mass as it is very useful in solving problems like this. The centre of mass can be present outside the physical bodies. The centre of mass is an inertial frame and it is at rest compared to the origin of the coordinate system.
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