Drops of water are thrown tangentially of the horizontal rim of a rotating wet umbrella. The rim is `3 ft` in diameter and is held `4 ft` above the ground and makes `14` revolutions in `33` seconds. Drops of water will meet the ground on a circle of diameter (in `ft`).

A small ball of mass 1 kg and charge (2)/(3)mu C is placed at the centre of a uniformly charged sphere of radius 1 m and charge (1)/(3)mC . A narrow smooth horizontal groove is made in the sphere from centre to suface as shown in figure. The sphere is made to rotate about its vertical diameter at a constant rate of (1)/(2pi) revolutions per second. Find the speed w.r.z ground (in m/s) with which the ball slides out from the groove. Neglect any magnetic force acting on ball.

A closed rectangular tank contains a certain amount of water. When the tank is placed on its 3 ft. by 4 ft. side, the height of the water in the tank is 5 ft. when the tank is placed on another side of dimension 4 ft. by 5 ft., what is the height, in feet, of the surface of the water above the ground?

A lamp is 50 ft above the ground. A ball is dropped from the same height from a point 30 ft away from the light pole. If ball falls a distance s=16 t^2 ft in t second, then how fast is the shadow of the ball moving along the ground 1/2 s later?

A surveyor on one bank of canal observed the image of the 4 inch and 17 ft marks on a vertical staff,which is partially immersed in the water and held against the bank directly opposite to him, coincides If the 17 ft mark and the surveyor's eye are both 6 ft above the water level ,estimate the width of the canal ,assuming that the reflective index of the water is 4//3 .Zero mark is at the bottom of the canal.

A rain drop of radius 2mm, falls from a height of 500 m above the ground. It falls with decreasing acceleration due to viscous resistance of air until half its original height. It attains its maximum (terminal ) speed, and moves with uniform speed there after. What is the work done by the gravitational force on the drop in the first half and second half of its journey ? Take density of water =10^(3)kg//m^(3) . What is the work done by the resistive force in the entire journey if its speed on reaching the ground is 10ms^(-1) ?