Question

# A phonograph turn table rotates at 50 rev/min. Its angular speed in rad/sec is

A

$8.164\mathrm{rad}.{\mathrm{sec}}^{-1}$

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B

$5.23\mathrm{rad}.{\mathrm{sec}}^{-1}$

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C

$52.3\mathrm{rad}.{\mathrm{sec}}^{-1}$

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D

$81.64\mathrm{rad}.{\mathrm{sec}}^{-1}$

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Solution

## The correct option is B $5.23\mathrm{rad}.{\mathrm{sec}}^{-1}$Angular speed Angular speed is defined as the rate of change of angular displacement, and it is expressed as follows: $\mathrm{\omega }=\frac{\mathrm{\theta }}{\mathrm{t}}$Here, $\mathrm{\theta }$ is the angular displacement, $\mathrm{t}$ is time and $\mathrm{\omega }$ is the angular speed.Find the angular speed of phonographIt is given that, a phonograph turn table rotates at $50\mathrm{rev}/\mathrm{min}$.We have to find the angular speed of the phonograph in $\mathrm{rad}/\mathrm{s}$.As we know that, $1$revolution means $2\pi or6.28$ radian and $1$ minute is equal to $60$ seconds.Therefore,$50\mathrm{rev}/\mathrm{min}=\frac{50×6.28}{60}$ $=5.24rad/s$ So, the angular speed of the phonograph turn table is approximate $5.23\mathrm{rad}/\mathrm{sec}$.Hence, option $\mathrm{B}$ is correct answer .

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