A square gate of size `1mxx1m` is hinged at its mid point. A fluid of density `rho` fill the space to the left of the gate. The force F required to hold the gate stationary is

A light semi cylindrical gate of radius R is pivoted aat its mid point O, of radius R as shown in the figure holding liquid of density rho . The force F required to prevent the rotation of the gate is equal to

The rectangualr wire- frame, shown in has a width d, mass m, resistance R and a large length. A uniform magnetic field B exists to the left of the frame. A constant force F starts pushing the frame into the magnetic field at t =0. (a) Find the acceleration of the frame when its speed has increased to v. (b) Show that after some time the frame will move with a constant velocity till the whole frame enters into the magnetic field. find this velocity v_0 . (c) show that the velocity at tiem t is given by v= v_0(1 - e^(-Ft/mv_0) .

Two liquids of densities rho_1 and rho_2(rho_2 = 3 rho_1) are filled up behind a square wall of side 6 m as shown in figure. Each liquid has a height of 3 m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (Assume that the liquids are not mixing)2

Two liquids of densities rho_1 and rho_2(rho_2 = 3 rho_1) are filled up behind a square wall of side 6 m as shown in figure. Each liquid has a height of 3 m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (Assume that the liquids are not mixing)2

Two liquids of densities rho_(1) and rho_(2)(rho_(2) = 2rho_(1)) are filled up behind a square wall of side 10 m as shown in the figure. Each liquids has a height of 5m. The ratio of the forces due to these liqyuids exeted on upper part MN to that at the lower part NO is (Assume that the liquids are not mixing):

Water is filled in a rectangular tank of size 3mxx2mxx1m . a) Find the total force exerted by the water on the bottom surface of the tank. b) Consider a vertical side of area 2mxx1m . Take a horizontal strip of wide deltax metre in this side, situated at a depth of x metre from the surface of water.Find the force by the water on this strip. c) Find the torque of the force calculate in part b) about the bottom edge of this side. d) Find the total force by the water on this side. e) Find the total torque by the water on the side about the bottom edge. neglect the atmospheric pressure and take =10ms^-2 .

During a heavy rain hailstones of average size 1.0 cm in diameter fall with an average speed of 20 m/s. Suppose 2000 hailstones strike every square meter of a 10mxx10m roof perpendicularly in one second and assume that the hailstones do not rebound. Calculate the average force exerted by the falling hailstones on the roof. Density of a hailstone is 900 kg/m^3

During a heavy rain hailstones of average size 1.0 cm in diameter fall with an average speed of 20 m/s. Suppose 2000 hailstones strike every square meter of a 10mxx10m roof perpendicularly in one second and assume that the hailstones do not rebound. Calculate the average force exerted by the falling hailstones on the roof. Density of a hailstone is 900 (kg)/m^3

A metallic rod of length 1m is rigidly clamped at its mid point. Longirudinal stationary wave are setup in the rod in such a way that there are two nodes on either side of the midpoint. The amplitude of an antinode is 2 xx 10^(-6) m . Write the equation of motion of a point 2 cm from the midpoint and those of the constituent waves in the rod, (Young,s modulus of the material of the rod = 2 xx 10^(11) Nm^(-2) , density = 8000 kg-m^(-3) ). Both ends are free.