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Question

Two uniform solid balls of the same density and radii r and 2r are dropped in air and are falling vertically downward. The terminal velocity of the ball of radius r is 1 cm/s, then the terminal velocity of the ball of radius 2r will be

A
1 cm/s
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B
4 cm/s
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C
3 cm/s
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D
2 cm/s
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Solution

The correct option is B 4 cm/s
Given:
Terminal velocity of the ball of radius r, vT1=1 cm/s
Terminal velocity of the ball of radius 2r, vT2=?

Terminal velocity is achieved when net force on the ball is zero.
Fnet=0
mg=FD
( FD= drag force due to air )
mg=6πrηvT
43πr3×ρ×g=6πrηvT
vT=2ρgr29η
For same material of ball,
vTr2
So, vT1vT2=(r1r2)2
1vT2=(r2r)2
vT2=4 cm/s

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