A tank with a square base of area 1.0 `m^2` is divided by a vertical partition in the middle. The bottom of the partition has a small-hinged door of area `20 cm^2`. The tank is filled with water in one compartment, and an acid (of relative density 1.7) in the other, both to a height of 4.0 m. compute the force necessary to keep the door close.

A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0 m, is whirled in a vertical circle with an angular velocity of 2 rev//s at the bottom of the circle. The cross-sectional area of the wire is 0.065 cm^2 . Calculate the elongation of the wire when the mass is at the lowest point of its path.

A long solenoid with 15 turns per cm has a small loop of area 2.0 cm^2 placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?

A hemi-spherical tank of radius 2 m is initially full of water and has an outlet of 12c m^2 cross-sectional area at the bottom. The outlet is opened at some instant. The flow through the outlet is according to the law v(t)=0.6sqrt(2gh(t)), where v(t) and h(t) are, respectively, the velocity of the flow through the outlet and the height of water level above the outlet and the height of water level above the outlet at time t , and g is the acceleration due to gravity. Find the time it takes to empty the tank.

A rectangular coil of area 5.0xx10^(-4) m^2 and 60 turns is pivoted about one of its vertical sides. The coil is in a radial horizontal field of 90 G (radial here means the field liners are in the plane of the coil for any rotation). What is the torsional constant of the hair spring connected to the coil if a current of 2.0 mA produces an angular deflection of 18^@ ?

A rigid and insulated tank of 3m^(3) volume is divided into two compartments. One compartment of volume of 2m^(3) contains an ideal gas at 0.8314 Mpa and 400 K while the second compartment of volume of 1m^(3) contains the same gas at 8.314 Mpa and 500 K. If the partition between the two compartments is rptured, the final temperature of the gas is :

Water is drained from a vertical cylindrical tank by opening a valve at the base of the tank. It is known that the rate at which the water level drops is proportional to the square root of water depth y , where the constant of proportionality k >0 depends on the acceleration due to gravity and the geometry of the hole. If t is measured in minutes and k=1/(15), then the time to drain the tank if the water is 4 m deep to start with is

Two parallel plate capacitors A and B have the same separation d= 8.85xx10^-4m between the plates. The plate area of A and B are 0.04m^2 and 0.02m^2 respectively. A slab of dielectric constant (relative permittivity) K=9 has dimensions such that it can exactly fill the space between the plates of capacitor B. A is then charged to a potential difference of 110V. Calculate the capacitance of A and the energy stored in it.

A vessel ABCD of 10 cm width has two small slits S_(1) and S_(2) sealed with idebtical glass plates of equal thickness. The distance between the slits is 0.8 mm. POQ is the line perpendicular to the plane AB and passing through O, the middle point of S_(1) and S_(2) . A monochromatic light source is kept at S, 40 cm below P and 2 m from the vessel, to illuminate the slits as shown in the figure. Calculate the position of the central bright fringe on the other wall CD with respect of the line OQ. Now, a liquid is poured into the vessel and filled up to OQ. The central bright fringe is fiund to be at Q. Calculate the refractive index of the liquid.