# A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45°, the speed of the car is: Option 1) 20 ms-1 Option 2) 30 ms-1 Option 3) 5 ms-1 Option 4) 10 ms-1

As we learnt in

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

$\theta=$ angle with which cycle leans

- wherein

*    radius of curve is small.

*    velocity of the cyclist is large.

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

$\theta = 45^{\circ}$

$r=90m$

$g=10m/s^{2}$

$\tan 45^{\circ}=\frac{v^{2}}{90\times 10}$

$V=30m/s$

Option 1)

20 ms-1

Incorrect

Option 2)

30 ms-1

Correct

Option 3)

5 ms-1

Incorrect

Option 4)

10 ms-1

Incorrect

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