Question

Two particle are situated on x axis having their masses 2g and 6g. If first particle is moved 9 cm forward. What must distance 6g be moved so that COM remains unchanged.

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Answer 1

Answer:

If x1 and x2 are the positions of masses m1 and m2, the position of the centre of mass is

m¡x1 + m2X2

given by Xcm If x1 changes by Axi and x2 changes by Ax2,

mi + m2

the change in Xcm will be

Axem m¡Ax1 + m2Ax2 .....(1)

mi + m2

Given Axcm = 0 and Axi d.

Using these values in eq.(i), we get mid +

m2 Ax2 = 0

or Ax2

m1d/m2

:. Distance moved by m2 = m1d/m2

Answer 2

Explanation:

Two particle are situated on x axis having their masses 2g and 6g. If first particle is moved 9 cm forward. What must distance 6g be moved so that COM remains unchanged.

We assume that in remaning part a disc of radius R and mass density ± σ is placed. Then

Total Moment of Inertia I = I1 + I2

To calculate I2 we use parallel axis theorem.