First slide

Viscous flow/Laminar flow

Question

A small sphere of mass m is dropped from a great height. After it has fallen 100 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 m of fall is

Moderate

A

Greater than the work done by air friction in the second 100 m
B

Less than the work done by air friction in the second 100 m
C

Equal to 100 mg
D

Greater than 100 mg

Solution

In the first 100 m body starts from rest and its velocity goes on increasing and after 100 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 $v = v_{T}$ .
Hence work done against air friction in the first 100 m is less than the work done in next 100 m.

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