question_answer

A conical pendulum of length 1 m makes an angle \[\theta ={{45}^{\text{o}}}\] 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 \[g=10\,m{{s}^{-1}}\])           [JEE Online 09-04-2017]

A) 0.2 m/s

B) 0.4 m/s

C) 2 m/s

D) 4 m/s

Correct Answer: C

Solution :

[c]

\[T\sin \theta \,=\frac{m{{v}^{2}}}{r}\]

\[T\cos \theta \,=mg\]

\[\tan \theta \,=\frac{{{v}^{2}}}{rg}\]

\[\theta ={{45}^{\text{o}}}\]

\[{{v}^{2}}=rg\]

\[\upsilon =\sqrt{rg}\,=\sqrt{0.4\,\times 10}\]

\[=2\,m/s\]