Question

a racing car complete 5 rounds of a circular track in 2 minutes. find the radius of the track,if the car has uniform centripetal acceleration of π² m/s²​

Answer 1

$\huge\boxed{ \underline{ \underline{ \bf{Answer}}}}$

$=>$ r = 144 m

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${ \underline{ \underline { \bf{Explanation}}}}$

Time for 5  rounds = 2 minutes.

                               = 2 × 60

                              = 120 Sec.

∴ Time for one round ( T ) = $\frac{120}{5} = 24 Sec$

∴ Frequency , n = $\frac{1}{T} = (\frac{1}{24} ) Sec$

centripetal acceleration = $\pi^{2} \:m/s^{2}$

we have to find out

r = ?

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centripetal acceleration = r  $w^{2}$

                                          = r $( 2 \pi n)^{2}$

                                          =   r ×$4\pi ^{2} \: n^{2}$

∴ r  =  $\frac{centripetal\:\: acceleration}{4\pi ^{2}\:n^{2}  }$

∴ r  =  $\frac{\pi ^{2} }{4\pi ^{2}\:(\frac{1}{24}) ^{2}  }$

     =  $\frac{(24)^{2} }{4}$

     =  $\frac{576}{4}$

∴ r =  144 m

∵ hence,

radius of the track = 144 m

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