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 1cm/s, then the terminal velocity of the ball of radius 2r will be
A
1cm/s
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B
4cm/s
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C
3cm/s
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D
2cm/s
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Solution
The correct option is B4cm/s Given: Terminal velocity of the ball of radius r, vT1=1cm/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, vT∝r2 So, vT1vT2=(r1r2)2 ⇒1vT2=(r2r)2 ⇒vT2=4cm/s