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 :

                \[T\sin \theta \,=\frac{m{{v}^{2}}}{r}\]                 \[T\cos \theta \,=mg\]                 \[\tan \theta \,=\frac{{{v}^{2}}}{rg}\] \[\theta ={{45}^{\text{o}}}\] \[{{v}^{2}}=rg\] \[\upsilon =\sqrt{rg}\,=\sqrt{0.4\,\times 10}\] \[=2\,m/s\]