A hemispherical bowl of radius R is placed upside down on a flat horizontal surface. There is a small hole at the top of the inverted bowl. Through the hole, a liquid of density `rho` is poured in. Exactly when the container gets full, water starts leaking from between the table and the edge of the container. Find the mass (m) of the contaienr.

A container filled with liquid up to height h is placed on a smooth horizontal surface. The container is having a small hole at the bottom. As the liquid comes out from the hole, the container moves in a backward direction with acceleration a and finally, when all the liquid is drained out, it acquires a velocity v . Neglect mass of the container. In this case

Consider a cuboidal vessel (2Rxx2RxxR) with as hemispherical cavity of radius R , kept at a horizontal smooth surface as shown in the figure. The vessel has very small hole of cross-sectional area "a". Now water of density rho is poured into space developed due horizontal surface adn vessel through hole very slowly. When the height of waer level is h , the vessel lifts off the surface and liquid leaks through space generated. (R=2m, rho=10^(3)kg//m^(3),m=9pi kg) . If the value of h is 5kcm , find the value of k . (Atmospheric pressure =10^(5)N//m^(2) ).

An air puck of mass m_(1) is tied to a string allowed to revolved in a circle of radius R on a frictionless horizontal table . The other end of the string passes through a small hole in the centre of the table , and a load of mass m_(2) is tied to the string? The suspended load remains in equilibrium while the pack on the tabletop revolves. a. Find the tension in the string b. Find the radial force acting on the puck c. Find the speed of the puck d. Qualitaively describe what will happen in the monsion of the puck if the value of m_(2) is somewhat increased by placing an additional load on it. e.Qualitaively describe what will happen in the monsion of the puck if the value of m_(2) is instead decreased removing a part from the hanging load.

Figure shows a body A at the top of a frictionless hemispherical inverted bowl of radius R. If the body starts slipping from the highest point, then the horizontal distance between the point where it leaves contact with sphere and the point at which the body was placed is

(i) In the arrangement shown in the figure, the tank has a large cross section and the pipes have much smaller cross section. The opening at A is unplugged and the water jet hits the ground surface at a horizontal distance x. (a) Find the level of water (h) in the tube B as water flows out of A. (b) Find x. (i) A flat horizontal surface has a small hole at its centre . A circular glass plate of radius R is placed symmetrically above the hole with a small gap h remainng between the plate and the surface A liquid enters the gap symmetrically from all sides and after travelling radially through the gap finally exits from the hole. The volume flow rate of the liquid coming out from the hole is Q (in m^(3)s^(-1) ). (a) If the flow speed just inside the circumference of the circular plate is V_(0) and the speed (V_(x)) of flow inside the gap at distance x(see figure) from the centre of the hole. (b) Write V_(x) in terms of Q, h and x.

In the figure shown, a solid sphere of mass 'm' and radius r is released from a height 6r to slide down a smooth surface. A plank of same mass 'm' touches the horizontal portion of the surface at the ground. The co-efficient of friction between the plank and the sphere is mu and that between the plank and the ground is mu//4 . Find the work done by the friction force between the plank and the ground till the sphere starts pure rolling on the plank. Neglect the height of the plank.