My Learning Cart
?
Categories
Account

Two particles of masses m1 and m2 are moving in a circular path with radii r1 an

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: Two particles of masses m1 and m2 are moving in a circular path with radii r1 and r2 respectively. If they have the same angular velocity, what is the ratio of their angular momenta?

Options:

  1. m1r1/m2r2
  2. m1/m2
  3. r1/r2
  4. m1r2/m2r1

Correct Answer: m1r1/m2r2

Solution: 

Angular momentum L = mvr, thus L1/L2 = (m1r1)/(m2r2) when ω is constant.

Two particles of masses m1 and m2 are moving in a circular path with radii r1 an

Practice Questions

Q1
Two particles of masses m1 and m2 are moving in a circular path with radii r1 and r2 respectively. If they have the same angular velocity, what is the ratio of their angular momenta?
  1. m1r1/m2r2
  2. m1/m2
  3. r1/r2
  4. m1r2/m2r1

Questions & Step-by-Step Solutions

Two particles of masses m1 and m2 are moving in a circular path with radii r1 and r2 respectively. If they have the same angular velocity, what is the ratio of their angular momenta?
  • Step 1: Understand that angular momentum (L) is calculated using the formula L = mvr, where m is mass, v is linear velocity, and r is the radius of the circular path.
  • Step 2: Recognize that if two particles are moving in a circular path with the same angular velocity (ω), their linear velocities (v) can be expressed as v = ωr.
  • Step 3: Substitute the expression for linear velocity into the angular momentum formula: L = m(ωr).
  • Step 4: For the first particle, the angular momentum L1 = m1(ωr1).
  • Step 5: For the second particle, the angular momentum L2 = m2(ωr2).
  • Step 6: To find the ratio of their angular momenta, calculate L1/L2 = (m1(ωr1))/(m2(ωr2)).
  • Step 7: Since ω is the same for both particles, it cancels out in the ratio, leading to L1/L2 = (m1r1)/(m2r2).
  • Angular Momentum – Angular momentum (L) is the product of a particle's mass (m), its velocity (v), and the radius (r) of its circular path. For two particles with the same angular velocity, the ratio of their angular momenta can be derived from their masses and radii.
  • Angular Velocity – Angular velocity (ω) is the rate of change of angular position of an object and is constant for both particles in this scenario, allowing for a direct comparison of their angular momenta based on mass and radius.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks