A spherical solid ball of volume V is made of | vedclass

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Question

(A) At terminal speed $(v_t)$,the net force acting on the ball is zero. The forces acting on the ball are its weight $(W)$ acting downwards,and the bu

Vedclass · Accepted Answer

$\sqrt {\frac{{Vg\left( {{\rho _1} - {\rho _2}} \right)}}{k}}$

Vedclass · Answer

(A) At terminal speed $(v_t)$,the net force acting on the ball is zero. The forces acting on the ball are its weight $(W)$ acting downwards,and the buoyant force $(B)$ and viscous force $(F_v)$ acting upwards.The condition for terminal speed is:$W = B + F_v$Substituting the expressions for the forces:$V \rho_1 g = V \rho_2 g + k v_t^2$Rearranging the equation to solve for $v_t^2$:$k v_t^2 = V \rho_1 g - V \rho_2 g$$k v_t^2 = Vg(\rho_1 - \rho_2)$Solving for $v_t$:$v_t^2 = \frac{Vg(\rho_1 - \rho_2)}{k}$$v_t = \sqrt{\frac{Vg(\rho_1 - \rho_2)}{k}}$Therefore,the terminal speed of the ball is $\sqrt{\frac{Vg(\rho_1 - \rho_2)}{k}}$.

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