The velocity of a small ball of mass 0.3 , g | vedclass

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Question

(C) When the velocity of the ball becomes constant,it is known as terminal velocity. At this state,the net force acting on the ball is zero.$F_V + F_B

Vedclass · Accepted Answer

$25$

Vedclass · Answer

(C) When the velocity of the ball becomes constant,it is known as terminal velocity. At this state,the net force acting on the ball is zero.$F_V + F_B = mg$Where $F_V$ is the viscous force,$F_B$ is the buoyant force,and $mg$ is the weight of the ball.$F_V = mg - F_B = V ho_B g - V ho_L g = V g (ho_B - ho_L)$Given: Mass $m = 0.3 \, g = 0.3 	imes 10^{-3} \, kg$,Density of ball $ho_B = 8 \, g/cc = 8000 \, kg/m^3$,Density of glycerine $ho_L = 1.3 \, g/cc = 1300 \, kg/m^3$.Volume $V = \frac{m}{ho_B} = \frac{0.3 	imes 10^{-3} \, kg}{8000 \, kg/m^3} = \frac{0.3}{8} 	imes 10^{-6} \, m^3$.$F_V = (8000 - 1300) 	imes (\frac{0.3}{8} 	imes 10^{-6}) 	imes 10$$F_V = 6700 	imes \frac{0.3}{8} 	imes 10^{-5} = 67 	imes \frac{0.3}{8} 	imes 10^{-3} = \frac{20.1}{8} 	imes 10^{-3} = 2.5125 	imes 10^{-3} = 25.125 	imes 10^{-4} \, N$.Thus,$x = 25.125$.

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