Question 47 of 210

A conical pendulum of length $l$ makes an angle $\theta =45^{\circ}$ with respect to $Z-$axis and moves in a circle in the $XY$ plane. The radius of the circle is $0.4m$ and its center is vertically below $O$. The speed of the pendulum, in its circular path, will be - $\left(Takeg=10m{s}^{-2}\right)$

A$0.2m{s}^{-1}$B$0.4m{s}^{-1}$C$2m{s}^{-1}$D$4m{s}^{-1}$

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Answer: (C) $2m{s}^{-1}$

$T\sin ⁡\theta =\dfrac{m{v}^{2}}{r}$

$T\cos ⁡\theta =mg$

$\tan ⁡\theta =\dfrac{{v}^{2}}{rg}$

$\theta ={45}^{o}$

${v}^{2}=rg$

$v=\sqrt{rg}=\sqrt{0.4\times 10}$

$v=2m{s}^{-1}$