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/m^{3}. 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})

The velocity of upper layer of water in a river is 36 kmh^{$$-$$1}. Shearing stress between horizontal layers of water is 10^{$$-$$3} Nm^{$$-$$2}. Depth of the river is __________ m. (Co-efficient of viscosity of water is 10^{$$-$$2} Pa.s)