Answer is in the file below
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We will apply the concepts of energy conservation to solve the problem. We know that gravitational potential energy is equivalent to the sum of translational kinetic energy and rotational kinetic energy. Additionally, the relation of the angular velocity with the tangential velocity will be determined to eliminate the angular term and obtain the expression of the Inertia in terms of the data given, therefore, we know that


The angular velocity in terms of tangential velocity and radius is defined as,

Replacing,

Multiplying by R^2,



Replacing with our values we have,


Option A 3......
... ........
To solve this problem it is necessary to apply the concepts related to pressure as a unit that measures the force applied in a specific area as well as pressure as a measurement of the density of the liquid to which it is subjected, its depth and the respective gravity.
The two definitions of pressure can be enclosed under the following equations

Where
F= Force
A = Area

Where,
Density
g = Gravity
h = Height
Our values are given as,


If we make a comparison between the lid and the tube, the diameter of the tube becomes negligible.
Matching the two previous expressions we have to

Re-arrange to find h




Therefore the height of water in the tube is 7.9cm