Question

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

• A. $\sqrt{3}:4$
• B. $4:\sqrt{3}$
• C. $2:\sqrt{3}$
• D. $\sqrt{3}:2$

Answer 1

Answer: (D)

Here, $\frac{r_1}{r_2}=\frac{6}{8},\frac{m_1}{m_2}=1$
$\frac{F_1}{F_2}=1$ or, $F_1=F_2$
or $\frac{m_1{v}_1^2}{r_1}=\frac{m_2{v}_2^2}{r^2}$
or $\frac{v_1^2}{v_2^2}=\frac{r_1}{r_2}\times \frac{m_2}{m_1}=\frac{6}{8}\times 1=\frac{3}{4}$
$\therefore \frac{v_1}{v_2}=\frac{\sqrt{3}}{2}$