GTA

A container of large uniform cross sectonal area A , resting on horizontal surface, holds two immiscible non viscous and incompresible liquids of density d and 2d , each of height H/2 as shown in the figure. Thelower density liquid is open to the atmospher having presure P_(0) . A tiny hole of area (s(sgt gtA) is punched on the vertical side of the container at a height h(hgtH/2) . Determine a.the initial speed of efflux of the liquid at the hole b. the horizontal disance x travelled by the liquid initially c. the height h_m at which at the hole should be punched so that the liquid travels the maximum distance x_(m) initially. also calculate x_(m) (neglect air resistance inte calculations).

In a magnetic field as shown, in Fig. two horizontal wires of same mass and length l_(1) and l_(2) are free to slide on different vertical rails with velocities v_(1) and v_(2) respectively. If the resistance of two circuits are same and a_(1) and a_(2) are acceleration of two horizontal wires respectively, the condition for a_(1)gta_(2) is