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An annular ring with inner and outer radii R₁and R₂ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring ,F₁/F₂is ,

Option 1)
1

Option 2)
$\frac{R_{1}}{R_{2}}$

Option 3)
$\frac{R_{2}}{R_{1}}$

Option 4)
$\left ( \frac{R_{1}}{R_{2}} \right )^{2}$

Answers (1)

best_answer

As we learnt in

Centripetal Force -

$F=4m\pi^{2}n^{2}r$

$F=\frac {4m\pi^{2}n^{2}r} {T^{2}}$

F = Centripetal force

$\omega=$ Angular velocity

n = frequency

- wherein

Force acts on the body along the radius and towards centre.

Centripetal force on particle = $mR\omega ^{2}$

$\therefore \: \: \: \frac{F_{1}}{F_{2}}= \frac{mR_{1}\omega ^{2}}{mR_{2}\omega ^{2}}= \frac{R_{1}}{R_{2}}$

Correct option is 2.

Option 1)

1

This is an incorrect option.

Option 2)

$\frac{R_{1}}{R_{2}}$

This is the correct option.

Option 3)

$\frac{R_{2}}{R_{1}}$

This is an incorrect option.

Option 4)

$\left ( \frac{R_{1}}{R_{2}} \right )^{2}$

This is an incorrect option.

Posted by

divya.saini

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