A stone of mass 20 g is projected from a rubber catapult of length 0.1 m and area of cross section 10^$$-$$6 m² stretched by an amount 0.04 m. The velocity of the projected stone is ______________ m/s.

(Young's modulus of rubber = 0.5 $$\times$$ 10⁹ N/m²)

The area of cross-section of a railway track is 0.01 m². The temperature variation is 10$$^\circ$$C. Coefficient of liner expansion of material of track is 10^$$-$$5/$$^\circ$$C. The energy stored per meter in the track is ____________ J/m.

(Young's modulus of material of track is 10¹¹ Nm^$$-$$2)

Consider a water tank as shown in the figure. It's cross-sectional area is 0.4 m². The tank has an opening B near the bottom whose cross-section area is 1 cm². A load of 24 kg is applied on the water at the top when the height of the water level is 40 cm above the bottom, the velocity of water coming out the opening B is v ms^-1.

The value of v, to the nearest integer, is ___________. [Take value of g to be 10 ms^-2]

Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes 0.01 cm³ of oleic acid per cm³ of the solution. Then you make a thin film of this solution (monomolecular thickness) of area 4 cm² by considering 100 spherical drops of radius $${\left( {{3 \over {40\pi }}} \right)^{{1 \over 3}}} \times {10^{ - 3}}$$ cm. Then the thickness of oleic acid layer will be x $$\times$$ 10^$$-$$14 m. Where x is ____________.