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The correct answer for determining the age of an old wooden idol is option-2, carbon dating. Carbon dating is a scientific method used to determine the age of organic materials, such as wood, by measuring the amount of carbon-14 present in the sample.
Carbon-14 is a radioactive isotope of carbon that is present in the Earth`s atmosphere. Living organisms, including trees and wooden idols, absorb carbon-14 during their lifetime. After an organism dies, it no longer absorbs carbon-14, and the existing carbon-14 begins to decay at a known rate.
By measuring the ratio of carbon-14 to carbon-12 in a sample of wood, scientists can determine the time that has elapsed since the death of the organism, and hence, the age of the wooden idol. This method is reliable for dating organic materials up to around 50,000 years old.
It should be noted that density (option-1), softness (option-3), and water content (option-4) are not appropriate methods for determining the age of a wooden idol. Therefore, the correct answer is option-2, carbon dating.