question_answer

Three masses of small size are attached by light inextensible strings of various lengths to a point 0 on the ceiling. All of the masses swing round in horizontal circles of various radii with the same angular frequency co (one such circle is drawn in the shown figure). Then pick up the correct statement.

A)  The vertical depth of each mass below point of suspension from ceiling is different.

B)  The radius of horizontal circular path of each mass is same.

C)  All masses revolve in the same horizontal plane.

D)  All the particles must have same mass.

Correct Answer: C

Solution :

[c] For conical pendulum of length l, mass m moving along horizontal circle as shown \[T\cos \theta =mg\]                                (i) \[T\sin \theta =m{{\omega }^{2}}l\sin \theta \]                (ii) Form equation (i) and (ii), \[l\cos \theta =\frac{g}{^{{{\omega }^{2}}}}\] \[l\cos \theta \]is the vertical distance of bob below 0 point of suspension. Hence, if \[\omega \]of all three pendulums are same. They shall revolve in same horizontal plane.