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AIIMS 2015
Exam
AIIMS
Year
2015
Subject
Physics
Chapter
Motion in Two Dimensions

AIIMS 2015 · Physics · Motion in Two Dimensions

The radii of circular paths of two particles of same mass are in...

The radii of circular paths of two particles of same mass are in ratio 6:86: 8 then what will be velocities ratio if they have a constant centripetal force?

Options

  1. A3:4\sqrt{3}: 4
  2. B4:34: \sqrt{3}
  3. C2:32: \sqrt{3}
  4. D3:2\sqrt{3}: 2

Correct answer

D. 3:2\sqrt{3}: 2

Step-by-step solution

 Here, r1r2=68,m1m2=1F1F2=1 or, F1=F2 or m1v12r1=m2v22r2 or v12v22=r1r2×m2m1=68×1=34∴v1v2=32\begin{aligned}& \text{ Here, } \frac{r_1}{r_2}=\frac{6}{8}, \frac{m_1}{m_2}=1 \\ & \frac{F_1}{F_2}=1 \text{ or, }F_1=F_2 \\ & \text{ or } \frac{m_1 v_1^2}{r_1}=\frac{m_2 v_2^2}{r_2}\\ & \text{ or } \frac{v_1^2}{v_2^2}=\frac{r_1}{r_2} \times \frac{m_2}{m_1}=\frac{6}{8} \times1=\frac{3}{4}\\ & \therefore \frac{v_1}{v_2}=\frac{\sqrt{3}}{2} \end{aligned}
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