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

Question

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) (M d1 g/d2) (B) M g(1-(d2/d1)) (C) (M(d1+d2)/g) (D) M d1 d2

Tardigrade Admin · Accepted Answer

Since, ball gains the constant velocity. Therefore, net force on the ball = zero. ⇒ Weight of the ball = Buoyancy force + Viscous force (Fv) ⇒ M g=(M/d1) × d2 × g+Fv ∴ Fv=M g(1-(d2/d1))

Q. The velocity of small ball of mass $M$ and density $d_{1} =$ when dropped a container filled with glycerine becomes constant after some time. If the density glycerine is $d_{2}$ , the viscous force acting on ball is

$\frac{M d _{1} g}{d _{2}}$

$M g (1 - \frac{d _{2}}{d _{1}})$

$\frac{M ( d _{1} + d _{2} )}{g}$

$M d_{1} d_{2}$

Since, ball gains the constant velocity.
Therefore, net force on the ball = zero.
$\Rightarrow$ Weight of the ball = Buoyancy force $+$ Viscous force $(F_{v})$
$\Rightarrow M g = \frac{M}{d _{1}} \times d_{2} \times g + F_{v}$
$∴ F_{v} = M g (1 - \frac{d _{2}}{d _{1}})$

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

d2​Md1​g​

Mg(1−d1​d2​​)

gM(d1​+d2​)​

Md1​d2​