Angular velocity of smooth parabolic wire y = 4c(x^2) about axis of parabola in vertical plane if bead of mass m does not slip at (a,b) will be

Is the parabola y ^(2) = 4x symmetrical about x-axis ?

A piece of wire is bent in the shape of a parabola y=kx^(2) (y-axis vertical) with a bead of mass m on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration a. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the y-axis is:

A small body is released from point A of smooth parabolic path y=x^(2) , where y is vertical axis and x is horizontal axis at ground, as shown. The body leaves the surface from point B. If g = 10ms^(-2) then what is the value of d (in m)?

A smooth wire frasme is in the shape of a parabola y = 5x^(2) . It is being rotated about y-axis with an angular velocity omega . A small bead of mass (m = 1 kg) is at point P and is in equilibrium with respect to the frame. Then the angular velocity omega is (g = 10 m//s^(2))

A piece of wire is bent in the shape of a parabola y = Kx^(2) (y - axis vorical) with a bead of mass m on it . The beat can side on the wire without friction , it stays the wire is now accleated parallel to the bead , where the bead can stay at rest with repect to the wire from the y - axis is

In the given figure, a smooth parabolic wire track lies in the xy -plane (vertical). The shape of track is defined by the equation y=x^(2) . A ring of mass m which can slide freely on the wire track, is placed at the position A (1,1) . The track is rotated with constant angular speed omega such that there is no relative slipping between the ring and the track. The value of omega is

A particle is placed at the lowest point of a smooth wire frame in the shape of a parabola, lying in the vertical xy-plane having equatioin x^(2) =5y(x,y are in meter). After slight displacement, the particle is set free. Find angular frequency of osciallation (in rad/sec) (Take g=10 m/ s^(2))

A uniform thin rod AB of mass M and length l attached to a string OA of length (l)/(2) is placed on a smooth horizontal plane and rotates with angular velocity omega around a vertical axis through O. A peg P is inserted in the plane in order that on striking it the bar will come exactly to rest

A uniform thin rod AB of mass M and length l attached to a string OA of length (l)/(2) is placed on a smooth horizontal plane and rotates with angular velocity omega around a vertical axis through O. A peg P is inserted in the plane in order that on stricking it the bar will come exactly to rest