A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 77 cm. Given that the bucket ascends in 1 minute 28 seconds with a uniform speed of 1.1 m/sec, calculate the number of complete revolutions the wheel makes in raising the bucket.

A car has wheels which are 80 cm in diameter. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?

A boy is cycling such that the wheel of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60cm, calculate the speed per hour with which the boy is cycling.

One end of a string is tied to a rigid support attached to roof and the other end is wound around a uniform wheel of radius r and mass m. The string is kept vertical and the wheel is released from rest. As the wheel descends show that (i) the tension in the string is one-third the weight of the wheel, (ii) the magnitude of the acceleration of the centre of mass is 2g/3 and (iii) the speed of the centre of mass is (4gh//3)^(1//2)

A cylindrical water tank of diameter 2.8 m and height 4.2 m is being fed by a pipe of diameter 7 cm through which water flows at the rate of 4 m s^(-1). Calculate, in minutes, the time it takes to fill the tank

A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60 cm, calculate the speed per hour with which the boy is cycling.

A bucket has top and bottom diameters of 40 cm and 20 cm respectively. Find the volume of the bucket if its depth is 12 cm. Also, find the cost of tin sheet used for making the bucket at the rate of Rs 1. 20\ p e r\ c m^2 .

A wheel of radius R=10 cm and moment of inertia I=0.05kg m^(2) is rotating about a fixed horizontal axis O with angular velocity omega_(0)=10rads^(-1) . A uniform riigid rod of mass m=3 kg and length l=50 cm is hinged at one end A such that it can rotate at end A in a vertical plane. End B of the rod is tied with a thread as shown in figure such that the rod is horizontal and is just in contact with the surface of rotating wheel. Horizontal distance between axis of rotation O of cylinder and A is equal to a = 30 cm . If the wheel stops rotating after one second after the thread has burnt, calculate coefficient of friction , mu between the rod and the surface of the wheel. (g = 10 ms^(-2))

The diameter of the front and the rear wheels of a tractor are 63 cm and 1.54 m respectively. The rear wheel is rotating at 24(6)/(11) revolutions per minute. Find : the revolutions per minute made by the front wheel.

A partical revolves in clockwise direction (as seen from point A) in a circle C of radius 1 cm and completes one revolution in 2 sec. The axis of the circle and the principal axis of the mirror M coincides, call it AB. The radius of curvature of the mirror of 20cm. Then, the direction of revolution (as seen from A) of the image of the partical and its speed is

A coin is placed on the horizontal surface of a rotation disc. The distance of the coin from the axis is 1 m and coefficient of friction is 0.5. If the disc starts from rest and is given an angular acceleration (1)/(sqrt(2)) rad / sec^(2) , the number of revolutions through which the disc turns before the coin slips is