Free daily NEET & JEE PYQs, quizzes & mock tests on TelegramJoin free →

NEET Physics: Centre of the mass of a two-particle system Practice Questions

10 free multiple-choice questions on Centre of the mass of a two-particle system (Rotational Motion) for NEET Physics, each with the correct answer and a step-by-step explanation. Attempt a question, then reveal the solution to check your reasoning.

Practice thousands more NEET questions in the app →

  1. Q1. The centre of mass of a system is defined as the point where the weighted average of the positions of all the particles is taken. Which statement is true regarding the centre of mass?

    • AIt is the location where the total force acts.
    • BIt is the point where the total momentum is conserved.
    • CIt is the point where the net external torque is zero.
    • DIt is the point where the system experiences zero resultant force.
    Show answer & explanation

    Correct answer: D — It is the point where the system experiences zero resultant force.

    The centre of mass is the average position of the mass distribution. While forces and torques relate to motion, the CM is fundamentally a property describing the distribution of mass. It is not necessarily where the resultant force acts or where zero torque exists (unless the system is in equilibrium).

  2. Q2. In a system of two particles, if the center of mass is stationary, it implies that:

    • AThe net external force acting on the system is zero
    • BThe relative distance between the particles is zero
    • CThe particles must have equal masses
    • DThe particles are moving with the same velocity
    Show answer & explanation

    Correct answer: A — The net external force acting on the system is zero

    If the center of mass is stationary, by the definition of the center of mass, the net external force acting on the entire system must be zero (F⃗ₙₑₜ = Ma⃗₍CM) = 0).

  3. Q3. Consider two particles A and B moving such that their centre of mass is stationary. This implies that the net external force acting on the system is:

    • AZero
    • BEqual to the sum of their individual forces
    • CDirected along the line connecting A and B
    • DEqual to the product of their masses
    Show answer & explanation

    Correct answer: A — Zero

    If the centre of mass of a system is stationary, the system is in equilibrium (or moving with constant velocity), meaning the net external force acting on the system must be zero (Newton's First Law extension).

  4. Q4. If two particles have equal masses, m₁ = m₂, what is the position of their center of mass?

    • AThe position of the particle further from the origin
    • BThe average of their positions only if they are separated equally
    • CThe weighted average of their positions
    • DThe midpoint between them
    Show answer & explanation

    Correct answer: D — The midpoint between them

    When the masses of the two particles are equal (m₁ = m₂), the center of mass coincides with the arithmetic mean (midpoint) of their positions: X₍CM) = (x₁ + x₂) / 2.

  5. Q5. If particle A has twice the mass of particle B, and they are separated by a distance d, how does the center of mass position relate to the positions of the two particles?

    • AThe CM is located at the midpoint
    • BThe CM is located at the position of the lighter particle
    • CThe CM is located closer to the heavier particle
    • DThe CM is located at the position of the heavier particle
    Show answer & explanation

    Correct answer: C — The CM is located closer to the heavier particle

    Since the mass of particle A (m_A = 2m_B) is greater than the mass of particle B (m_B), the center of mass will be shifted closer to the particle with the larger mass (Particle A).

  6. Q6. If the center of mass of a two-particle system remains stationary, what must be true about the relative motion of the two particles?

    • AThe particles must be moving at the same velocity.
    • BThe particles must be moving in opposite directions.
    • CThe net external force on the system must be zero.
    • DThe distance between the particles must be constant.
    Show answer & explanation

    Correct answer: C — The net external force on the system must be zero.

    The motion of the center of mass is governed by the external forces acting on the system (F⃗ₑₓₜ = Mₜₒₜₐₗ a⃗₍CM)). If the center of mass is stationary (a⃗₍CM) = 0), it implies that the net external force on the system is zero, regardless of the internal motion.

  7. Q7. Two particles of masses M and 2M are placed at positions 0 m and 3 m respectively along a straight line. What is the position of the center of mass of this system?

    • A2.0 m
    • B1.5 m
    • C0.5 m
    • D1.0 m
    Show answer & explanation

    Correct answer: B — 1.5 m

    The position of the center of mass (X₍CM)) is calculated using the formula: X₍CM) = (M · x₁ + 2M · x₂) / (M + 2M). Substituting the values: X₍CM) = (M · 0 + 2M · 3) / (3M) = 6M / 3M = 2 m.

  8. Q8. Consider a system of two particles. If the center of mass is stationary, what must be true regarding the motion of the individual particles?

    • AThe particles must be moving in the same direction
    • BThe particles must have equal and opposite velocities
    • CThe particles must have zero velocity
    • DThe particles must be moving with equal speed
    Show answer & explanation

    Correct answer: C — The particles must have zero velocity

    If the center of mass of a system is stationary, it implies that the total momentum of the system is zero. If the system is isolated (no external forces), the center of mass must have zero acceleration. For the simplest case of two particles, this often implies zero velocity if they start from rest.

  9. Q9. The velocity of the center of mass of a two-particle system is given by the formula:

    • AV₍CM) = (m₁ v₁ + m₂ v₂)/(m₁ - m₂)
    • BV₍CM) = (m₁ + m₂)/(m₁ + m₂) (v₁ + v₂)
    • CV₍CM) = (m₁ v₁ + m₂ v₂)/(m₁ + m₂)
    • DV₍CM) = (m₁ v₁)/(m₂ v₂)
    Show answer & explanation

    Correct answer: C — V₍CM) = (m₁ v₁ + m₂ v₂)/(m₁ + m₂)

    The velocity of the center of mass is the weighted average of the velocities of the individual particles, weighted by their masses: V₍CM) = (m₁ v₁ + m₂ v₂) / (m₁ + m₂).

  10. Q10. Which of the following quantities is invariant for a system of two particles when only internal forces act?

    • AThe kinetic energy of the individual particles
    • BThe total linear momentum of the system
    • CThe relative velocity between the particles
    • DThe linear momentum of the individual particles
    Show answer & explanation

    Correct answer: B — The total linear momentum of the system

    The total linear momentum of a system remains constant if no net external force acts on it (conservation of momentum). This property holds true for the center of mass motion as well.

Keep going — practice on Padhai Karlo

Padhai Karlo gives you unlimited NEET practice: chapter-wise questions, timed quizzes, and full mock tests with an All-India Rank — free to start.

Get the free Android app →

More Rotational Motion topics

← All Rotational Motion practice