A particle move on an circular overbridge with constant speed. The friction coefficient varies so that the speed remains constant. Which of the following graph shows the magnitude of friction

A small body of mass $m$ slides down from the top of a hemisphere of radius $r$. The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is

A stone tied to a string of length $L$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is

A small sphere of mass $m$ is suspended by a light and inextensible string of length $l$ from a point $O$ fixed on a smooth inclined plane of inclination $\theta $ with the horizontal. The sphere is moving in a circle on the incline as shown. If the sphere has a velocity $u$ at the top most position $A$ . Then,

A bucket tied at the end of a $1.6\, m$ long string is whirled in a vertical circle with constant speed. What should be the minimum speed so that the water from the bucket does not spill, when the bucket is at the highest position …….. $m/sec$ (Take $g = 10\,m/{\sec ^2}$)