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Centre of Mass & Linear Momentum formula sheet

Every formula in the Centre of Mass & Linear Momentum chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 31 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Centre of mass of particles

COM of particles
5× asked, last 2026
r⃗cm=∑mir⃗i∑mi,xcm=∑mixiM\vec r_{cm}=\frac{\sum m_i\vec r_i}{\sum m_i},\qquad x_{cm}=\frac{\sum m_ix_i}{M}
One axis at a time, signed coordinates. Equal masses: plain average of positions.
Two particles
2× asked, last 2024
m1r1=m2r2,r1=m2 dm1+m2m_1r_1=m_2r_2,\qquad r_1=\frac{m_2\,d}{m_1+m_2}
Distances from the COM; nearer the heavier mass. COM fixed: m1Δx1=m2Δx2m_1\Delta x_1=m_2\Delta x_2.
Composite bodies
3× asked, last 2025
xcm=m1x1+m2x2+…m1+m2+…x_{cm}=\frac{m_1x_1+m_2x_2+\dots}{m_1+m_2+\dots}
Each part as a point mass at its own COM. Plate: mass ∝ area; rod: mass ∝ length.
Balancing on a support
1× asked, last 2022
∑mig di (clockwise)=∑mjg dj (anticlockwise)\sum m_ig\,d_i\ (\text{clockwise})=\sum m_jg\,d_j\ (\text{anticlockwise})
Torques about the pivot; each weight acts at its COM.

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Practise Centre of Mass & Linear Momentum

27 more formulas in 5 topics

Centre of mass of continuous bodies, Motion of the centre of mass, Conservation of linear momentum, Impulse and Variable mass: rockets and belts. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Centre of mass of continuous bodies

  • Continuous body3×
  • Non-uniform rod3×
  • Ring arcs1×
  • Discs2×
  • Hemispheres1×
  • Cones and triangle
  • Removed part (negative mass)4×
  • Hole touching the rim

Motion of the centre of mass

  • Velocity and acceleration of COM2×
  • Second law for a system1×
  • Projectile exploding in mid-air
  • Kinetic energy of a system1×

Conservation of linear momentum

  • Momentum and kinetic energy5×
  • Conservation of momentum7×
  • Splitting from rest and recoil5×
  • Nucleus splitting
  • Explosion into three pieces2×
  • Man on a boat or plank
  • Sticking together2×

Impulse

  • Impulse–momentum theorem8×
  • Rebound4×
  • Oblique impact on a wall1×
  • FF–tt and pp–tt graphs2×
  • Stream of bullets or balls3×

Variable mass: rockets and belts

  • Thrust2×
  • Rocket going up1×
  • Mass picked up at speed vv1×

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About 55 past JEE Main questions from this chapter, with instant answer checking and step-by-step solutions where available. Free, and you can start without signing up.

Practise Centre of Mass & Linear Momentum

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Version 1, October 2026. Free to share for study, as it is. Please don't sell it or remove the PrepWiser name.

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