The velocity of a small ball of mass m and de | vedclass

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Question

(A) When the ball moves with a constant velocity (terminal velocity),the net force acting on it is zero.The forces acting on the ball are:$1$. Weight

Vedclass · Accepted Answer

$m g(1 - \frac{d_{2}}{d_{1}})$

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(A) When the ball moves with a constant velocity (terminal velocity),the net force acting on it is zero.The forces acting on the ball are:$1$. Weight of the ball $(W = m g)$ acting downwards.$2$. Buoyant force $(F_{B})$ acting upwards.$3$. Viscous force $(F_{V})$ acting upwards.At terminal velocity,the forces are balanced:$F_{V} + F_{B} = m g$$F_{V} = m g - F_{B}$The buoyant force is equal to the weight of the displaced liquid:$F_{B} = V 	imes d_{2} 	imes g$,where $V$ is the volume of the ball.Since $V = \frac{m}{d_{1}}$,we have $F_{B} = \frac{m}{d_{1}} 	imes d_{2} 	imes g$.Substituting this into the force equation:$F_{V} = m g - (\frac{m}{d_{1}} 	imes d_{2} 	imes g)$$F_{V} = m g (1 - \frac{d_{2}}{d_{1}})$

The velocity of a small ball of mass $m$ and density $d_{1}$,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:

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