A lead shot of 1 mm diameter falls through a long column of glycerine. The variation of its velocity v with distance covered is represented by:
A
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B
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C
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D
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Solution
The correct option is A When the lead shot falls through glycerine column, drag force (FD) and buoyant force (FB) act on it along upwards direction. However its weight (mg) acts downwards.
FD=6πrηv
At t=0, v=0 as the shot was just released, thus FD=0.
The lead shot gets accelerated downwards and at time t
a=mg−FB−FDm
As time elapses, distance covered, i.e. x increases and the magnitude of acceleration decreases.
⇒ velocity of lead shot increases at a slower rate with increase in x, until →Fnet=0 and a constant terminal velocity (vT) is achieved.