A bucket containing water is tied to a rope of length 2.5 m and rotated in a vertical circle in wuch a way that the winter in it does not spill,what is the minimum velocity of the bucket at which this happens and how many rotations per minutes is it making then?(Take `g=10 m s^(-2)`).

A small stone, of mass 0.2 kg, tied to a massless, inextensible string, is rotated in vertical circle of radius 2 m. if the particle is just able to complete the vertical circle, what is its speed at the highest point of its circular path? How would this speed get effected if the mass of the stone is increased by 50%? (Take g = 10 ms^(-2) )

The power of a motor pump is 5 kW. How much water per minute the pump an raise to height of 20 m ? Take g = 10ms ^-2 .

From a rope of length 15 m, two pieces of length 4 (3)/(5)m and 2 (3)/(10) m, are cut off The left over rope is converted into a circle. What is the radius of the circle?

A massless string of length 1.2 m, has a breaking strength of 2 kg wt. A stone of mass 0.4 kg, tied to one end of the string, is made to move in a vertical circle, by holding the other end in the hand. Can the particle describe the vertical circle? (Take g = 10 m s^-2 )

A small stone of mass 200 g is tied to one end of a string of length 80 cm . Holding the other end in hand , the stone is whirled into a vertical circle What is the minimum speed that needs to be imparted at the lowest point of the circular path , so that the stone is just able to complete the vertical circle ? what would be the tension at the lowest point of circular path ? (Take g = 10 m//s^(2) ) .

A particle of mass 150 g is attached to one end of a massless inextensible string It is made to describe a vertical circle of radius 1 m When the string is making an angle of 48.2^(@) with the vertical , its instantaneous speed is 2 m//s What is the tension in the string in this position ? Would this particle be able to complte its circular path?(Take g=10 m s^(-2) ).

A ball of 0.03 m diameter and 0.3 kg in weight is attached to the end of a thin string of 0.46 m length. If it is rotate uniformly in a horizontal circle at the rate of 15 revolutions per second, what is the tension in the string? Take pi^2 = 9.87 ).

A tank containing water upto the height 15 m from the bottom of the tank. Find the speed and horizontal range of the water jet coming out through an orifice which is at 5 m above the bottom of the wtawer tank . {(Use g = 10 m s^-2)

A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0 m, is whirled in a vertical circle with an angular velocity of 2 rev//s at the bottom of the circle. The cross-sectional area of the wire is 0.065 cm^2 . Calculate the elongation of the wire when the mass is at the lowest point of its path.