A metallic sphere of radius `1.0 xx 10^(-3) m` and density `1.0 xx 10^(4) kg//m^(3)` enters a tank of water, after a free fall through a distance of h in the earth's gravitational field. If its velocity remains unchanged after entering water, determine the value of `h`. Given: coefficient of viscosity of water `= 1.0 xx 10^(-3) N s//m^(2), g = 10ms^(-12)` and density of water `= 1.0 xx 10^(3) kg//m^(3)`.

Explanation

To solve the problem step by step, we will follow the logical sequence of calculations based on the information provided.

### Step 1: Determine the velocity attained after free fall
The velocity \( v \) attained by the sphere after falling through a height \( h \) can be calculated using the formula for free fall:
\[ v = \sqrt{2gh} \]
where:
...