Question

A conical pendulum of length $1\,m$ makes an angle $\theta = 45^{\circ}$ 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 $g = 10 \, ms^{-2}$)

• A. 0.4 m/s
• B. 4 m/s
• C. 0.2 m/s
• D. 2 m/s

Answer 1

Answer: (D)

2 m/s

Answer 2

$T$ sin $\theta=\frac{mv^{2}}{r}$
$T$ cos $\theta=\frac{v^{2}}{rg}$
tan $\theta=\frac{v^{2}}{rg}$
$\theta=45^{\circ}$
$v^{2}=rg$
$\upsilon=\sqrt{rg}=\sqrt{0.4\times10}$
$=2$ m/s