Isostasy

Sir George Everest

Step 1: The chapter describes a famous survey carried out in India to study plumb-line deflection near the Himalayas. Step 2: This survey was conducted by Sir George Everest, the Surveyor-General of India, in 1854. Step 3: The world's highest peak, Mount Everest, is named after him as a tribute. Step 4: Pratt studied the gravitational data from Everest's survey but did not conduct the survey himself. Step 5: Airy and Bouguer were not involved in this Indian survey. So Sir George Everest is correct.

Kaliana

Step 1: The chapter describes the geodetic survey conducted by Sir George Everest. Step 2: The survey measured the difference in latitude between two places – Kalianpur and Kaliana, which were 603 km apart. Step 3: Kaliana is near the Himalayan mountain system, so the plumb line there was attracted (deflected) by the mountains. Step 4: Kalianpur is further away from the Himalayas, so its plumb line was not deflected. Step 5: Kanpur, Shimla, and Delhi were not mentioned in this context. So Kaliana is the correct answer.

Archimedes' Principle (Hydrostatic Equilibrium)

Step 1: Airy followed the Law of Floatation when proposing his concept. Step 2: He used Archimedes' Principle, which states that a solid floating in a liquid displaces a mass of liquid equal to its own mass. Step 3: He argued that lighter sial blocks float on denser sima in hydrostatic equilibrium – just like a boat floats on water. Step 4: Newton's Law of Gravitation is a different concept related to attraction between masses. Step 5: Pascal's Law and Conservation of Energy are unrelated to floating of crustal blocks. So Archimedes' Principle is correct.

An iceberg floating in the sea

Step 1: Airy used the iceberg analogy to explain how mountains stay balanced. Step 2: When an iceberg floats in the sea, one part is above the water level and nine parts are immersed in water (freeboard to draught ratio is 1:9). Step 3: Similarly, mountains have a large portion ('roots') extending deep into the denser substratum, just like the submerged part of the iceberg. Step 4: A stone sinks – it does not float, so it is not a valid analogy. Step 5: A balloon and oil are about buoyancy in gases/liquids, not the same concept. So iceberg is the correct analogy.