Critical Speed & Looping

A body of mass 'm' attached at the end of a string is just completing the loop in a vertical circle. The apparent weight of the body at the lowest point in its path is

($g$ = gravitational acceleration)

A bucket containing water is revolved in vertical circle of radius r. To prevent the water from falling down, the period of revolution required is ($g$ = gravitational acceleration)

A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height $h$ as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height $h = \alpha R$. The value of $\alpha$ is ______

In case of vertical circular motion of a particle by a thread of length $r$ if the tension in the thread is zero at an angle $30^\circ$ shown in figure, the velocity at the bottom point $(A)$ of the circular path is (g = gravitational acceleration)

A point mass ' $m$ ' attached at one end of a massless, inextensible string of length ' $l$ ' performs a vertical circular motion and the string rotates in vertical plane, as shown in the diagram. The increase in the centripetal acceleration of the point mass when it moves from point A to point C is [ $g =$ acceleration due to gravity.]

A body of mass ‘m’ connected to a massless and unstretchable string goes in vertical circle of radius ‘R’ under gravity g. The other end of the string is fixed at the center of circle. If velocity at top of circular path is $n\sqrt{gR}$, where, n ≥ 1, then ratio of kinetic energy of the body at bottom to that at top of the circle is:

A bob of mass $m$ is suspended at a point $O$ by a light string of length $l$ and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity $v_0$ at the point ' A ', the string becomes slack when, the bob reaches at the point ' $D$ '. The ratio of the kinetic energy of the bob at the points B and C is _________.

A body of mass '$m$' attached at the end of a string is just completing the loop in a vertical circle. The apparent weight of the body at the lowest point in its path is ( $g$ = gravitational acceleration)

A bucket containing water is revolved in a vertical circle of radius $r$. To prevent the water from falling down, the minimum frequency of revolution required is

($g =$ acceleration due to gravity)

A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point Q is A while angular position of point Q is $\alpha$ with respect to point P. Which of the following graphs represent the correct relation between A and $\alpha$ when ball goes from Q to R?

A pendulum of length 2 m consists of a wooden bob of mass 50 g. A bullet of mass 75 g is fired towards the stationary bob with a speed v. The bullet emerges out of the bob with a speed $\frac{v}{3}$ and the bob just completes the vertical circle. The value of v is ___________ ms______1. (if g = 10 m/s2).

A body attached to one end of a string performs motion along a vertical circle. Its centripetal acceleration, when the string is horizontal, will be [$g =$ acceleration due to gravity]

A particle is released on a vertical smooth semicircular track from point X so that OX makes angle $\theta$ from the vertical (see figure). The normal reaction of the track on the particle vanishes at point Y where OY makes angle $\phi$ with the horizontal. Then: