Questions in Motion in A Plane

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	A ball is moving to and fro about the lowest point A of a smooth hemispherical bowl. If it is able to rise up to a height of 20 cm on either side of A, its speed at A must be (Take $g = 10 m/s^2$, mass of the body 5 g)
	A stone of mass m is tied to a string and is moved in a vertical circle of radius r making n revolutions per minute. The total tension in the string when the stone is at its lowest point is
	As per given figure to complete the circular loop what should be the radius if initial height is 5 m
	A coin, placed on a rotating turn-table slips, when it is placed at a distance of 9 cm from the centre. If the angular velocity of the turn-table is trippled, it will just slip, if its distance from the centre is
	When a ceiling fan is switched off its angular velocity reduces to 50% while it makes 36 rotations. How many more rotation will it make before coming to rest (Assume uniform angular retardation)
	A body crosses the topmost point of a vertical circle with critical speed. Its centripetal acceleration, when the string is horizontal will be
	A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is 3 times the weight of the pendulum bob. What is the maximum displacement of the pendulum of the string with respect to the vertical
	A particle is moving in a vertical circle. The tensions in the string when passing through two positions at angles $30^o$ and $60^o$ from vertical (lowest position) are $T_1$ and $T_2$ respectively. then
	A particle is kept at rest at the top of a sphere of diameter 42 m. When disturbed slightly, it slides down. At what height ‘h’ from the bottom, the particle will leave the sphere
	The coordinates of a moving particle at any time ‘t’ are given by $x = \alpha t^3$ and $y = \beta t^3$. The speed of the particle at time ‘t’ is given by

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