The velocity of small ball of mass M and density d1 when dropped a container filled with glycerine…

Q: The velocity of small ball of mass M and density d1 when dropped a container filled with glycerine becomes constant after some time. If the density glycerine is d2, the viscous force acting on ball is

(a) $ \displaystyle \frac{M g d_1}{d_2} $

(b) $ \displaystyle M g(1-\frac{ d_2}{d_1}) $

(c) $ \displaystyle \frac{M( d_1 – d_2 )}{g} $

(d) $ \displaystyle \frac{M d_1}{d_2} $

Ans: (b)

Sol:

Viscous force = Weight – Buoyancy

= V d1 g – V d2g

= V d1g(1-d2/d1)

= M g (1 – d2/d1)