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Question
A small sphere of mass m is dropped from great height. After it has fallen 100 metres, it has attained its terminal velocity and continue to fall at that speed. The work done by air friction against the sphere during the first 100 metres of fall is:
A small sphere of mass m is dropped from great height. After it has fallen 100 metres, it has attained its terminal velocity and continue to fall at that speed. The work done by air friction against the sphere during the first 100 metres of fall is:
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Solution
The correct option is B less than the workdone by air friction in the second 100 meters.
When the sphere falls through air, initially its velocity keeps on increasing till it attains a maximum velocity called terminal velocity(vT). The air friction, i.e. viscous force which is proportional to velocity, is low in the beginning and maximum at v=vT. Hence, work done against air friction in the first 100 metres is less than the work done in the next 100 metres.
When the sphere falls through air, initially its velocity keeps on increasing till it attains a maximum velocity called terminal velocity(vT). The air friction, i.e. viscous force which is proportional to velocity, is low in the beginning and maximum at v=vT. Hence, work done against air friction in the first 100 metres is less than the work done in the next 100 metres.
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