# A conical pendulum of length 1 m makes an angle  w.r.t. Z-axis and moves in a circle in the XY plane.  The radius of the circle is 0.4 m and its center is vertically below O.  The speed of the pendulum, in its circular path, will be : (Take g=10 ms−2) Option 1) 0.4 m/s Option 2) 4 m/s Option 3)  0.2 m/s Option 4)  2 m/s

As we learnt in

If friction is also present in banking of road -

$\frac{V^{2}}{rg}=\frac{\mu+tan\theta}{1-\mu tan \theta}$

$\theta=$ angle of banking

$\mu=$ coefficient of friction

V = velocity

- wherein

Maximum speed on a banked frictional road

$V=\sqrt{\frac{rg(\mu+tan\theta)}{1-\mu tan\theta}}$

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

$Tcos\theta=mg$                                        (ii)

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

$v^{2}=gr$

$v=\sqrt{gr}=\sqrt{0.4\times10}=2ms^{-1}$

Correct option is 4.

Option 1)

0.4 m/s

This is an incorrect option.

Option 2)

4 m/s

This is an incorrect option.

Option 3)

0.2 m/s

This is an incorrect option.

Option 4)

2 m/s

This is the correct option.

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