A conical pendulum of length 1 m makes an angle θ=45° 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 the point of suspension O. The speed of the pendulum, in its circular path, will be (Take g=10 m s⁻²)

Question

Accepted Answer

(2) 2 m/s. Idea: for a conical pendulum the string's tension both holds the bob up and turns it, and dividing the two balance equations gives tan θ=(v²)/(rg). Vertically: T cos θ=mg. Horizontally: T sin θ=(mv²)/r. Dividing, tan θ=(v²)/(rg), so v=√rg tan θ. With r=0.4 m, g=10 m/s² and tan 45°=1: v=√0.4×10×1=√4=2 m/s. The length 1 m is not needed once the radius is given — and strictly the two are not consistent, since a 1 m string at 45° would sweep a radius of 0.707 m. The radius and the angle are what the working uses.

A conical pendulum of length 1 m makes an angle θ=45° 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 the point of suspension O. The speed of the pendulum, in its circular path, will be (Take g=10 m s⁻²)

Step-by-step solution

Why the other options are wrong