The area of cross-section of a large tank is 0.5 m². It has a narrow opening near the bottom having area of cross-section 1 cm². A load of 25 kg is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is 40 cm above the bottom, will be ___________ cms^$$-$$1. [Take g = 10 ms^$$-$$2]

The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of 5 $$\times$$ 10^$$-$$4 is __________ kJ/m³. Assume that material is elastic upto the linear strain of 5 $$\times$$ 10^$$-$$4.

The elongation of a wire on the surface of the earth is 10^$$-$$4 m. The same wire of same dimensions is elongated by 6 $$\times$$ 10^$$-$$5 m on another planet. The acceleration due to gravity on the planet will be ____________ ms^$$-$$2. (Take acceleration due to gravity on the surface of earth = 10 ms^$$-$$2)

An ideal fluid of density 800 kgm^$$-$$3, flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from a to $${a \over 2}$$. The pressure difference between the wide and narrow sections of pipe is 4100 Pa. At wider section, the velocity of fluid is $${{\sqrt x } \over 6}$$ ms^$$-$$1 for x = ___________. (Given g = 10 ms^$$-$$2)