A bead of mass m stays at point on a wire bent in the shape of a parabola and rotating with angular speed (see figure). The value of is (neglect friction):
Step 1: Given data and required figure
The equation of a parabola is,
Mass of a bead
Angular speed of a bead
The coordinate point is given as
Acceleration due to gravity
The required figure for given problem is shown below:
Step 2: Finding the value of
We have the equation of parabola
Differentiating with respect to we get,
Now resolving the forces on a bead we get,
And also:
Now dividing both the forces, we get
Therefore the angular speed is equal to
Hence, option(D) is the correct answer.