Statement $I :$ A cyclist is moving on an unbanked road with a speed of $7\, kmh ^{-1}$ and takes a sharp circular turn along a path of radius of $2 \,m$ without reducing the speed. The static friction coefficient is $0.2$ . The cyclist will not slip and pass the curve $\left( g =9.8\, m / s ^{2}\right)$
Statement $II :$ If the road is banked at an angle of $45^{\circ}$, cyclist can cross the curve of $2\, m$ radius with the speed of $18.5\, kmh ^{-1}$ without slipping.
In the light of the above statements, choose the correct answer from the options given below.
JEE MAIN 2021, Difficult
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Statement $I :$
$v _{\max }=\sqrt{\mu Rg }=\sqrt{(0.2) \times 2 \times 9.8}$
$v _{\max }=1.97\, m / s$
$7 \,km / h =1.944\, m / s$
Speed is lower than $v _{\max }$, hence it can take safe turn.
Statement $II:$
$v _{\max }=\sqrt{ Rg \left[\frac{\tan \theta+\mu}{1-\mu \tan \theta}\right]}$
$=\sqrt{2 \times 9.8\left[\frac{1+0.2}{1-0.2}\right]}=5.42 \,m / s$
$18.5 \,km / h =5.14 \,m / s$
Speed is lower than $v _{\max }$, hence it can take safe turn.
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