Question

if conical pendulum has mass m length l, revolving in a horizontal circle with constant speed v. show that the variation of its mass does not affect its period of motion.​

Answer 1

Answer:

Balance the forces

In vertical direction

A component of tension is balancing weight of pendulum

$mg =t \cos( \alpha ) \\ t = mg \sec( \alpha )$

Now one component in horizontal direction is keeping pendulum in circular motion . Or it is equal to centrifugal force

$t \sin( \alpha ) = m \frac{ {v}^{2} }{r} \\ \\ mg \sec( \alpha ) \sin( \alpha ) = m \frac{ {v}^{2} }{r } \\ \\ {v}^{2} = gr \tan( \alpha )$

v is independent of m and

T = 2πr/v will also be independent of m .