The tangential acceleration at particle at the lowest position is 

A small bucket containing water is rotated in a vertical circle of radius $R$ by means of a rope. $v$ is velocity of bucket at highest point. Then water does not fall down if:

A bucket filled with water is tied to a rope of length $0.5\ m$ and is rotated in a circular path in vertical plane. the least velocity it should have at the lowest point of circle so that water does not spill is $(g=10ms^{-2})$:

A very small particle rests on the top of a hemisphere of radius $20\ cm$. The smallest horizontal velocity to be given to it, if it is to leave the hemisphere without sliding down its surface taking $g = 9.8 m/s^{2}$ is:

The minimum centripetal force required to rotate a body mass $m$ in a vertical circle of radius $r$ is

A particle of mass m is rotating by means of a string in a vertical circle. The difference in the tensions at the bottom and the top towards completion of a full revolution would be

Four objects of masses m, 2m , 3m and 4m are attached to a string of length L=2 metres and rotated vertically with a speed of $\sqrt(5Lg)$, pick out the most appropriate one:

An object suspended by a string has a critical velocity at the top most point of a circle. It will complete a full circle 

A block of mass $m$ at the end of a string is whirled round in a vertical circle of radius $R$. The critical speed of the block at the top of its swing below which the string would slacken before the block reaches the top is:

A bob of mass $100\ g$ tied at the end of a string of length $50\ cm$ is revolved in a vertical circle with constant speed of $1\ ms^{-1}$. When the tension in the string is $0.7N$, the angle made by the vertical is $(g=10\ ms^{-2})$

A weightless thread can withstand tension upto 30 N.A. stone of mass 0.5kg is tied to it and is revolved in a circular path of radius 2m i n a vertical plane. If $g=10m/s^2$, then the maximum angular velocity of the stone can be;-

An inclined plane ends into vertical loop of radius $R$. A particle is released from height $3R$. Can it loop the loop?

A block of mass $m$ at the end of a string is whirled round in a vertical circle of radius $r$. The critical speed of the block at the top of its swing below which the string would slacken before block reaches the top is

The maximum tension that an inextensible ring of radius 1 m and mass density 0.1 kg ${ m }^{ -1 }$ can bear is 40 N . The maximum angular velocity with which it can be rotated in a  circular path is 

A body is allowed to slide on a frictionless track from rest under-gravity.The track ends in a circular of diameter D. What should be the mini-mum height of the body in terms of D.          So that it may successfully complete the loop?

A body is a allowed to slide down a frictionless track from rest position at its top under gravity. The track ends in a circular loop of diameter $D$. Then, the minimum height of the inclined track  (in terms of $D$ ) so that it may complete successfully the loop is:

The length of simple pendulum is $1m$ and mass of its bob is $50 gram$. The bob is given  sufficient velocity so that the bob describes vertical circle whose radius equal to length of pendulum, the tension in the string at lowest extreme position is:

A weightless thread can bear tension up to $3.7kg-wt$. A stone of mass $500g$ is tied to it and revolved in a circular path of radius $4$m in a verticle plane. If $g=10m/s^2$, then the maximum angular velocity of the stone will be:

A body attached to a string of length describes a vertical circle such that it is just able to cross the highest point. Find the minimum velocity at the bottom of the circle.

A bucket is whirled in a vertical circle with a string attached to it. The water in the bucket does not fall down even when the bucket is inverted at the top of its path. We can say that in this position.