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A cyclist is moving with velocity 20m/s . if he wants to take a cicular turn of radius 40 m then for his safe turn what should be the value of angle made by the cyclist with vertical ( $g = 10 m/s^2$ )
Option: 1
$60 \degree$

Option: 2
$75 \degree$

Option: 3
$45 \degree$

Option: 4
$30 \degree$

Answers (1)

best_answer

As we have learned

Bending a Cyclist -

From figure.

$R\sin\theta=\frac{mv^{2}}{r}$ (i)

$R\cos\theta=mg$ (ii)

(i) & (ii)

$tan\theta=\frac{v^{2}}{rg}$

$\theta=tan^{-1}\left( \frac{v^{2}}{rg} \right )$

V = velocity

r = radius of track

$\theta=$ angle with which cycle leans

- wherein

* radius of curve is small.

* velocity of the cyclist is large.

From diagram

$R \sin \theta = \frac{mv^2 }{r}.....(1 )$

$R \cos \theta = mg.....(2 )$

$\tan \theta = \frac{v^2 }{rg} = \frac{20 \times 20 }{40 \times 10 } = 1$

$\theta = 45 \degree$

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Gunjita

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