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A system consists of two identical particles one particle is at rest and the other particle has an acceleration 'a'. The centre of mass of the system has an acceleration of
- a)2a
- b)a
- c)a/2
- d)a/4
Correct answer is option 'C'. Can you explain this answer?
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Solution:
Given, two identical particles, one is at rest and the other has an acceleration a.
Acceleration of centre of mass (a_cm) = (m1a1 + m2a2)/(m1+m2)
As the particles are identical, m1 = m2 = m (say)
a_cm = (m1*a1 + m2*a2)/(m1+m2)
a_cm = (m*a + m*0)/(m+m)
a_cm = a/2
Therefore, the correct option is C.
Explanation:
The centre of mass of a system is the point where the entire mass of the system is assumed to be concentrated. The position of the centre of mass depends only on the positions and masses of the particles in the system, and not on their velocities or accelerations.
Here, we have two identical particles, one is at rest and the other has an acceleration a. As the particles are identical, their masses are also identical.
The acceleration of the centre of mass is given by the formula:
a_cm = (m1a1 + m2a2)/(m1+m2)
where m1 and m2 are the masses of the particles and a1 and a2 are their respective accelerations.
In this case, m1 = m2 = m and a1 = 0 (as one particle is at rest) and a2 = a (as the other particle has an acceleration of a).
Substituting the values, we get:
a_cm = (m1a1 + m2a2)/(m1+m2)
a_cm = (m*a + m*0)/(m+m)
a_cm = a/2
Hence, the acceleration of the centre of mass is a/2.
Given, two identical particles, one is at rest and the other has an acceleration a.
Acceleration of centre of mass (a_cm) = (m1a1 + m2a2)/(m1+m2)
As the particles are identical, m1 = m2 = m (say)
a_cm = (m1*a1 + m2*a2)/(m1+m2)
a_cm = (m*a + m*0)/(m+m)
a_cm = a/2
Therefore, the correct option is C.
Explanation:
The centre of mass of a system is the point where the entire mass of the system is assumed to be concentrated. The position of the centre of mass depends only on the positions and masses of the particles in the system, and not on their velocities or accelerations.
Here, we have two identical particles, one is at rest and the other has an acceleration a. As the particles are identical, their masses are also identical.
The acceleration of the centre of mass is given by the formula:
a_cm = (m1a1 + m2a2)/(m1+m2)
where m1 and m2 are the masses of the particles and a1 and a2 are their respective accelerations.
In this case, m1 = m2 = m and a1 = 0 (as one particle is at rest) and a2 = a (as the other particle has an acceleration of a).
Substituting the values, we get:
a_cm = (m1a1 + m2a2)/(m1+m2)
a_cm = (m*a + m*0)/(m+m)
a_cm = a/2
Hence, the acceleration of the centre of mass is a/2.
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A system consists of two identical particles one particle is at rest and the other particle has an acceleration a. The centre of mass of the system has an acceleration ofa)2ab)ac)a/2d)a/4Correct answer is option 'C'. Can you explain this answer?
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