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  • A cyclist goes on a round a circular path with constant speed with 30m/s . If the radius of the path is 90m then the angle made by him with vertical will be:  

A cyclist goes on a round a circular path with constant speed with 30m/s . If the radius of the path is 90m then the angle made by him with vertical will be:

 

Option: 1

300


Option: 2

450


Option: 3

200


Option: 4

100


Answers (1)

best_answer

 

 

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

So,

 

 

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

R\cos \theta =mg                      (ii)

by (i) and (ii)

\tan \theta =\frac{v^{2}}{rg}\Rightarrow \theta = \tan ^{-1}(\frac{v^{2}}{rg}) = \tan ^{-1}(\frac{30\times 30}{10\times 90}) = \tan ^{-1}(1)

\theta = 45^{\circ}

Posted by

Riya

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