A wheel of radius R is trapped in a mud pit and spinning. As the wheel is spinning , it splashes mud blobs with initial speed `u` from various points on its circumference . the maximum height from the center of the wheel , to which mud blob can reach is

Completion type Question : A body is thrown vertically up from the ground with a speed u and it reaches its maximum height h at time t = t_0 . The height to which it would have risen at t = (t_0)/2 is………

A wheel of radius R=2m performs pure rolling on a rough horizontal surface with speed v=10 m/s . In the figure shown, angle theta is angular position of point P on wheel reaches the maximum height from ground. Find the value of "sec"theta (take g=10 m//s^(2) ).

A string is wrapped around a wheel of radius r. The axis of the wheel is horizontal and its M.I. about the axis is I. Weight mg is tied to free end of the string which is released to fall down from rest position. The angular velocity of the wheel after it has fallen through distance .h. will be

A boy ‘A’ is running on a circular track of radius R. His friend, standing at a point O on the circumference of the track is throwing balls at speed u = sqrt(gR) . Balls are being thrown randomly in all possible directions. Find the length of the circumference of the circle on which the boy is completely safe from being hit by a ball.

Figure shows a student, sitting on a stool that can rotate freely about a vertical axis. The student, initially at rest, is holding a bicycle wheel whose rim is loaded with lead and whose moment of inertia is I about its central axis. The wheel is rotating at an angular speed omega_i from an overead perspective, the rotation is counter clockwise. The axis of the wheel point vertical, and the angular momentum vecL_i of the wheel points vertically upward. The student now inverts the wheel, as a result, the student and stool rotate about the stool axis. With what angular speed and direction does the student then rotate? (The moment of inertia of the student+stool+wheel system about the stool axis is I_0 )