A stone of mass 100 g is rotating in a circular orbit of radius 50 cm with a frequency 5 r.p.s.find the centripetl force acting on the stone.

A body of mass m moves in a circular path of radius r with a velocity v. Find the expression for the centripetal force F acting on the body by using method of dimensions.

A body of mass m is moving in a circle of radius r with angular velocity omega . Find an expression for the centripetal force f acting on it using method of dimensional analysis.

A body of mass 20g is rotating around a pole 50 cm away with a frequency 5 r.p.s.Find the rotational kinetic energy of the body.

An artificial satellite is revolving around a planet fo mass M and radius R, in a circular orbit of radius r. From Kepler's third law about te period fo a satellite around a common central bdy, square of the period of revolution T is proportional to the cube of the radius of the orbit r. Show usingn dimensional analysis, that T = k/R sqrt((r^3)/(g)) , where k is a dimensionless constant and g is acceleration due to gravity.

A paticle of mass m is executing uniform circular motion on a path of radius r. If p is the magnitude of its linear momentum, then the radial force acting on the particle is

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 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) )

Give the magnitude and direction of the net force acting on a stone of mass 0.1kg:- lying on the floor of a train which is accelerating with 1 m s^-2 , the stone being at rest relative to the train.Neglect air resistance throughout.