Explain how fish survive in frozen ponds and define pitch of a micrometer screw gauge with calculation of observed reading.

Fish can survive under frozen pond surfaces due to the anomalous expansion of water. Water is densest at $4^\circ \text{C}$. As the surface of a pond freezes, the colder, less dense water ($0^\circ \text{C}$ to $4^\circ \text{C}$) remains at the top, eventually freezing. The denser water at $4^\circ \text{C}$ sinks to the bottom, forming a layer of liquid water where fish can survive.

The pitch of a micrometer screw gauge is the distance moved by the spindle for one complete rotation of the thimble. A standard micrometer with 50 divisions on the thimble typically has a pitch of $0.5 \text{mm}$.

The pitch of the gauge is $\boxed{\text{0.5 mm}}$.

First, determine the observed reading from the micrometer scale.
Main scale reading: The last visible mark on the main scale is $10 \text{mm}$. The $0.5 \text{mm}$ mark after $10 \text{mm}$ is also visible.
Main scale reading $= 10.5 \text{mm}$.

Thimble scale reading: The line on the main scale aligns with the $37^\text{th}$ division on the thimble scale.
Thimble scale reading $= 37$.

Least count of the micrometer:

Observed reading:

Given positive error:

Correct reading:

Converting to centimeters:

The correct reading on the scale is $\boxed{\text{1.073 cm}}$.

When liquid soap is introduced into the water drop, the surface tension of the water decreases. Surface tension is responsible for holding the water drop in a spherical shape. With reduced surface tension, the cohesive forces within the drop become weaker, causing the drop to spread out and become flatter on the surface.