Two particles having mass '$$M$$' and '$$m$$' are moving in a circular path with radius '$$R$$' and '$$r$$' respectively. The time period for both the particles is same. The ratio of angular velocity of the first particle to the second particle will be
In a conical pendulum the bob of mass '$$\mathrm{m}$$' moves in a horizontal circle of radius '$$r$$' with uniform speed '$$\mathrm{V}$$'. The string of length '$$\mathrm{L}$$' describes a cone of semi vertical angle '$$\theta$$'. The centripetal force acting on the bob is ( $$\mathrm{g}=$$ acceleration due to gravity)
A ball of mass '$$\mathrm{m}$$' is attached to the free end of a string of length '$$l$$'. The ball is moving in horizontal circular path about the vertical axis as shown in the diagram.
The angular velocity '$$\omega$$' of the ball will be [ $$\mathrm{T}=$$ Tension in the string.]
A particle performing uniform circular motion of radius $$\frac{\pi}{2} \mathrm{~m}$$ makes '$$\mathrm{x}$$' revolutions in time '$$t$$'. Its tangential velocity is