Aircraft
A boy is driving a model aircraft with the help of a light inextensible cord of length L . He does so by moving the free end of the cord with a constant speed in a horizontal circle of radius r . As a result the aircraft moves in another horizontal circle of radius R ( R > r ) with a constant speed v at an altitude h above the plane containing circular path of the other end held. Suppose centres of both circles lie on same vertical line. Considering the air drag to be present; find the lift force of air on the aircraft. ( Take m as the mass of the aircraft and g as acceleration due to gravity)
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1 solution
If you experiment it physically , you will see the string's end held to hand and other end is not making a frustum ( a cut cone to be precise) in deed while rotating. Rather it crosses the side making 'z' like shape .
So it will give Lift= mg +( m v^2 h )/ ( R^2 + R×r) By comparing the centrifugal forces in the both circles. And lastly put the value obtained of (r×R) which will give you ( L^2-R^2-r^2-h^2 )/2