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Exam
NEET
Subject
Physics
Chapter
Motion in Two Dimensions

NEET · Physics · Motion in Two Dimensions

Two particles of masses m_1 and m_2 are moving in concentric...

Two particles of masses m1m_1 and m2m_2 are moving in concentric circles of radii r1r_1 and r2r_2 respectively. It is given that the ratio of their masses is m1:m2=1:2m_1 : m_2 = 1 : 2 and the ratio of their radii is r1:r2=4:1r_1 : r_2 = 4 : 1. If they have the same time period of revolution, the ratio of their centripetal forces F1:F2F_1 : F_2 is:

Options

  1. A2:12 : 1
  2. B1:81 : 8
  3. C8:18 : 1
  4. D1:21 : 2

Correct answer

A. 2:12 : 1

Step-by-step solution

Time period TT is the same for both particles, so their angular velocity ω=2πT\omega = \dfrac{2\pi}{T} is also the same.

The centripetal force is given by F=mrω2F = m r \omega^2.

The ratio of their centripetal forces is:
F1F2=(m1m2)(r1r2)(ω1ω2)2\dfrac{F_1}{F_2} = \left(\dfrac{m_1}{m_2}\right) \left(\dfrac{r_1}{r_2}\right) \left(\dfrac{\omega_1}{\omega_2}\right)^2

Substitute the given values:
F1F2=(12)×(41)×(1)2\dfrac{F_1}{F_2} = \left(\dfrac{1}{2}\right) \times \left(\dfrac{4}{1}\right) \times (1)^2

F1F2=21\dfrac{F_1}{F_2} = \dfrac{2}{1}

Thus, the ratio F1:F2F_1 : F_2 is 2:12 : 1.

Answer: 2:12 : 1
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