Rotational Motion Question 56

Question: Consider a system of two particles having masses m1 and m2 . If the particle of mass m1 is pushed towards the mass centre of particles through a distance d, by what distance would the particle of mass m2 move so as to keep the mass centre of particles at the original position?

[AIPMT (S) 2004]

Options:

A) m1m1+m2d

B) m1m2d

C) d

D) m2m1d

Show Answer

Answer:

Correct Answer: B

Solution:

  • The system of two given particles of masses m1 and m2.

    Initially the centre of mass

    rCM=m1r1+m2r2m1+m2 …(1)

    When mass m1 moves towards centre of mass by a distance d, then let mass m2 moves a distance d’ away from CM to keep the CM in its initial position.

    So, rCM=m1(r1d)+m2(r2+d)m1+m2

    Equating Eqs.

    (i) and (ii), we get

    m1r1+m2r2m1+m2=m1(r1d)+m2(r2+d)m1+m2

    m1d+m2d=0

    d=m1m2d

    NOTE: If both the masses are equal i.e., m1=m2, then second mass will move a distance equal to the distance at which first mass is being displaced.



NCERT Chapter Video Solution

Dual Pane