An object is located at 2 km beneath the surface of the water. If the fractional compression $${{\Delta V} \over V}$$ is 1.36%, the ratio of hydraulic stress to the corresponding hydraulic strain will be ____________. [Given : density of water is 1000 kgm^$$-$$3 and g = 9.8 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 ____________.

The disc of mass M with uniform surface mass density $$\sigma$$ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position $${x \over 3}{a \over \pi },{x \over 3}{a \over \pi }$$ where x is _____________. (Round off to the Nearest Integer).

[a is an area as shown in the figure]

The image of an object placed in air formed by a convex refracting surface is at a distance of 10 m behind the surface. The image is real and is at $${{{2^{rd}}} \over 3}$$ of the distance of the object from the surface. The wavelength of light inside the surface is $${2 \over 3}$$ times the wavelength in air. The radius of the curved surface is $${x \over {13}}$$ m. The value of 'x' is ___________.