A conical pendulum of length l makes an angle θ = 45 ° with respect to Z - axis and moves in a…

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

1. $0.2 \mathrm{m} {\mathrm{s}}^{-1}$
2. $0.4 \mathrm{m} {\mathrm{s}}^{-1}$
3. $2 \mathrm{m} {\mathrm{s}}^{-1}$
4. $4 \mathrm{m} {\mathrm{s}}^{-1}$

Solution

$T\sin \theta =\frac{m{v}^2}{r}$

$T\cos \theta =mg$

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

$\theta ={45}^o$

$v^2=rg$

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

$v=2 \mathrm{m} {\mathrm{s}}^{-1}$
 

Asked in: JEE Main 2017 (09 Apr Online)

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