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Two hollow cylinders of radii ' $1 m$ ' and ' $2 m$ ' respectively have common geometrical aixs as shown in the figure.

A fly starts with a constant speed ' $v$ ' and hits the outer cylinder at ' X ' from inside. If both the cylinder starts rotating with an angular velocity of ' $1 rad/s$ '. The fly strikes another point ' Y ' where the distance between ' X ' and ' Y ' is $10 \mathrm{~cm}$ . Assuming the fly moves radially, find the speed of the fly.

Option: 1
$10m/s$

Option: 2
$20 m/s$

Option: 3
$30 m/s$

Option: 4
$40 m/s$

Answers (1)

best_answer

Let the fly crosses the inner cylinder at time, $t=0$ and reaches the outer at time, $t=t$ . As the fly moves radially.

$\begin{aligned} (R-r)=t v \\ t=\frac{(R-r)}{v} \\ t=\frac{1}{v} \end{aligned}$

If the cylinder is rotating with an angular velocity of ' $\omega$ ', then angular displacement of the cylinder in the same time interval well be:-

$\theta=\omega t=(1)\left(\frac{1}{v}\right)$

$\frac{l}{R}=\left ( \frac{1}{v} \right )\\$

$\begin{aligned} & v=\frac{R}{l}=\frac{2}{10 \times 10^{-2}}=\frac{2}{0.1} \\ & v=20 \mathrm{~m} / \mathrm{s} \end{aligned}$

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Rakesh

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