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If the radii of circular paths of two particles of same mass are in the ratio of $1: 2$, then to have a constant centripetal force, the ratio of their speeds should be
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Verified Answer
The correct answer is:
$1: \sqrt{2}$
Centripetal force
$F=\frac{m v^2}{R}$ or $v=\sqrt{\frac{F R}{m}}$ or , $v \propto \sqrt{R}$ as mass ' $m$ ' and force ' $F$ '
is constant. $\frac{R_1}{R_2}=\frac{1}{2}$
$\therefore \frac{\mathrm{V}_1}{\mathrm{~V}_2}=\sqrt{\frac{\mathrm{R}_1}{\mathrm{R}_2}}=\sqrt{\frac{1}{2}}=\frac{1}{\sqrt{2}}$
$F=\frac{m v^2}{R}$ or $v=\sqrt{\frac{F R}{m}}$ or , $v \propto \sqrt{R}$ as mass ' $m$ ' and force ' $F$ '
is constant. $\frac{R_1}{R_2}=\frac{1}{2}$
$\therefore \frac{\mathrm{V}_1}{\mathrm{~V}_2}=\sqrt{\frac{\mathrm{R}_1}{\mathrm{R}_2}}=\sqrt{\frac{1}{2}}=\frac{1}{\sqrt{2}}$
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