A mass m rotating freely in a horizontal circle of radius 1 m on a frictionless smooth table supports a stationary mass 2m, attached to the

other end of the string passing through smooth hole O in table, hanging vertically. Find the angular velocity of rotation.

Solution) for block rotating on table...

T = mv2/r where T is tension

and for block hanging vertically,

T= mg

mg= mv2/r

v = root ( rg)

  =root(10)

w= v/r=root(10)/1 = root ( 10)= 3.2 rad/sec