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  • Statement I : A cyclist is moving on an unbanked road with the speed of 7 kmh-1 and takes a sharp circular turn along the path of radius of 2m without reducing the speed. The static friction coefficent is 0.2. The cyclist will not slip

Statement I : A cyclist is moving on an unbanked road with the speed of 7 kmh-1 and takes a sharp circular turn along the path of radius of 2m without reducing the speed. The static friction coefficent is 0.2. The cyclist will not slip and pass the curev ( g= 9.8 m/s2) Statement II : If the road is bnaked at an angle of 45^{\circ} , cyclist will not slip and pass the curve of 2m radius with the speed of 18.5  kmh-1  without slipping.
Option: 1 Statement I is correct and Statement II is incorrect
Option: 2 both statement I and statement II are false
Option: 3 both statement I and statement II are true
Option: 4 statement I is incorrect and statement II is correct

Answers (1)

best_answer

For statement I


\mathrm{v}_{\max }=\sqrt{\mu \mathrm{Rg}}=\sqrt{(0.2) \times 2 \times 9.8}
\mathrm{v}_{\max }=1.97 \mathrm{~m} / \mathrm{s} 7 \mathrm{~km} / \mathrm{h}=1.944 \mathrm{~m} / \mathrm{s}
Speed is lower than \mathrm{v}_{\max }, hence it can take safe
turn.

For statement II

\\ \mathrm{v}_{\max }=\sqrt{\operatorname{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]}\\ \mathrm{v}_{\max }=5.42 \mathrm{~m} / \mathrm{s} 18.5 \mathrm{~km} / \mathrm{h}=5.14 \mathrm{~m} / \mathrm{s} 
Speed is lower than \mathrm{v}_{\max }, hence it can take safe turn.

So 

both statement I and statement II are true

Posted by

avinash.dongre

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