MOTION IN A PLANE Set 3

A bob of mass is suspended by a massless string of length . The horizontal velocity at position is just sufficient to make it reach the point . The angle at which the speed of the bob is half of that at , satisfies

For a particle in uniform circular motion, thee acceleration at a point on the circle of radius R is (Here is measured from the x-axis)

A man can thrown a stone 100 m away. The maximum height to which he can throw vertically is

Roads are banked on curves so that

A piece of wire is bent in the shape of a parabola -axis vertical) with a bead of mass on it. The bead can side 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 -axis with a constant acceleration . The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the -axis is

Figure shows a body of mass moving with a uniform speed along a circle of radius . The change in velocity in going from to is

A particle starts from the origin of coordinates at time and moves in the plane with a constant acceleration in the -diretion. Its equation of motion is . Its velocity component in the -direction is

A body is revolving with a uniform speed in a circle of radius . The tangential acceleration is

A project is projected with a velocity of making an angle of with horizontal. The equation for the trajectory is where is height, is horizontal distance, and are constants. The ratio is

If the equation for the displacement of a particle moving on a circular path is given by , where is in radians and in seconds, then the angular velocity of the particle after from its start is