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The playing track of a CD is made out of a number of concentric circles with the inner...

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The playing track of a CD is made out of a number of concentric circles with the inner circle having a radius of 2 cm and the outer circle having a radius of 6 cm. The CD is rotating at 5 revolutions per second and takes 25 minutes to completely play.

Find the total length of the playing track in km, correct to one dp, given that there is 7500 revolutions in 25 minutes.

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In 1 sec number of revolutions=5

so in 25 minute number of revolutions=25x60x5=7500

According to problem radial distance travelled =4 cm

Thus in every revolution radius change=4/7500

=`533xx10^(-4)` cm

Thus

`r_1=2.0 cm`

`r_2=r_1+5.33xx10^(-4) cm`

`r_3=r_1+5.33xx10^(-4) cm`

`.........`

`r_{7500)=r_{7499}+5.33xx10^(-4) cm`

`` Thus

`S_7500=c_1+c_2+....+c_7500`

`=2pir_1+2pir_2+...+2pir_7500`

`=2pi(r_1+r_2+....+r_7500)`

`=2xx(22/7) xx(2+(2+5.33xx10^(-4))+.............+(2+7499xx5.33xx10^(-4)))`

`=(44/7){(7500/2)(2xx2+(7499)xx5.33xx10^(-4)}` 

`=(44/7){3750(4+3.997)}cm`

`=.269km`

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