Question

A cyclist while negotiating a circular path with speed ms-1 is found to bend an angle by 30°with vertical. what is the radius of circular path?(given g=10ms-2)

Answer 1

$\Huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

Derivation For Bending Of Cyclist

$\Large \leadsto {\sf{R Sin\theta \: = \: \frac{mv^2}{r}}---(1)}$

And

$\Large \leadsto {\sf{R Cos \theta \: = \: mg}---(2)}$

Now, Divide (1) by (2)

$\Large \leadsto {\sf{\frac{\cancel{R} Sin \theta}{\cancel{R} Cos \theta} \: = \: \frac{\cancel{m}v^2}{\frac{r}{\cancel{m}g}}}}$

$\LARGE \implies {\boxed{\red{\sf{Tan \theta \: = \: \frac{v^2}{rg}}}}}$

$\rule{200}{2}$

A.T.Q,

Angle = 30°

Velocity = 1 m/s

Put Values in formula :

$\Large \leadsto {\sf{Tan 30^{\circ} \: = \: \frac{(1)^2}{r(10)}}}$

As Tan 30° = 1/√3

$\Large \leadsto {\sf{r \: = \: \frac{\sqrt{3}}{1} \: \times \: \frac{1}{10}}}$

$\Large \leadsto {\sf{r \: = \: \frac{\sqrt{3}}{10}}}$

$\LARGE {\boxed{\red{\sf{r \: = \: 0.1732 \: m}}}}$