NEET Solved Paper 2018 Question 42

Question: A small sphere of radius ‘r’ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to [NEET - 2018]

Options:

A) $ {r^{5}} $

B) $ {r^{2}} $

C) $ {r^{3}} $

D) $ {r^{4}} $

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Answer:

Correct Answer: A

Solution:

Power $ \text{=6}\pi \eta rV _{T}\cdot V _{T}=6\pi \eta rV_T^{2} $

$ V _{T}\propto r^{2} $

$ \Rightarrow \text{Power }\propto {r^{5}} $