A small spherical ball of radius 0.1 mm and density 10⁴ kg m^$$-$$3 falls freely under gravity through a distance h before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of h will be ___________ m.

(Given g = 10 ms^$$-$$2, viscosity of water = 1.0 $$\times$$ 10^$$-$$5 N-sm^$$-$$2).

A liquid of density 750 kgm^$$-$$3 flows smoothly through a horizontal pipe that tapers in cross-sectional area from A₁ = 1.2 $$\times$$ 10^$$-$$2 m² to A₂ = $${{{A_1}} \over 2}$$. The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is ___________ $$\times$$ 10^$$-$$3 m³s^$$-$$1.

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.