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Question: Answered & Verified by Expert
A small sphere of mass $m$ is dropped from a great height. After it has fallen $100 \mathrm{~m}$, it has attained its terminal velocity and continues to fall at that speed. The work done by air friction against the sphere during the first $100 \mathrm{~m}$ of fall is
PhysicsMechanical Properties of FluidsJEE Main
Options:
  • A Greater than the work done by air friction in the second $100 \mathrm{~m}$
  • B Less than the work done by air friction in the second $100 \mathrm{~m}$
  • C Equal to $100 \mathrm{mg}$
  • D Greater than $100 \mathrm{mg}$
Solution:
2760 Upvotes Verified Answer
The correct answer is: Less than the work done by air friction in the second $100 \mathrm{~m}$
In the first $100 \mathrm{~m}$ body starts from rest and its velocity goes on increasing and after $100 \mathrm{~m}$ it acquire maximum velocity (terminal velocity). Further, air friction i.e. viscous force which is proportional to velocity is low in the beginning and maximum at $v=v_r$.
Hence work done against air friction in the first $100 \mathrm{~m}$ is less than the work done in next $100 \mathrm{~m}$.

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