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14/09/2021 11:50 am
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The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is d/2, then the viscous force acting on the ball will be :
(1) \(\frac{Mg}{2}\)
(2) Mg
(3) \(\frac{3}{2}\)Mg
(4) 2Mg
1 Answer
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14/09/2021 11:52 am
Correct answer: (1) \(\frac{Mg}{2}\)
Explanation:
Mass = M
Density of ball = d
Density of glycerine = \(\frac{d}{2}\)
FB = Vsρℓg = v \(\frac{d}{2}\)g
Fg = Mg = vdg
for constant velocity, FB = 0
∴ FB + Fv = Mg
Fv = Mg - FB = Vdg - \(\frac{Vdg}{2}\)
= \(\frac{Vdg}{2}\) = \(\frac{Mg}{2}\)