A hydraulic lift is shown in the figure. The | vedclass

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(D) Given radii: $r_A = 10 \,cm = 0.1 \,m$, $r_B = 100 \,cm = 1 \,m$, $r_C = 5 \,cm = 0.05 \,m$.Weight placed on piston $A$ is $F_A = m_A g = 2g$.Acco

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None of the above

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(D) Given radii: $r_A = 10 \,cm = 0.1 \,m$, $r_B = 100 \,cm = 1 \,m$, $r_C = 5 \,cm = 0.05 \,m$.Weight placed on piston $A$ is $F_A = m_A g = 2g$.According to Pascal's law, the pressure is transmitted equally throughout the fluid: $\frac{F_A}{A_A} = \frac{F_B}{A_B} = \frac{F_C}{A_C}$.Since $A = \pi r^2$, we have $\frac{F_A}{r_A^2} = \frac{F_B}{r_B^2} = \frac{F_C}{r_C^2}$.For piston $B$: $F_B = F_A 	imes \left(\frac{r_B}{r_A}ight)^2 = 2g 	imes \left(\frac{1}{0.1}ight)^2 = 2g 	imes 100 = 200g$.Thus, the mass that can be lifted by $B$ is $m_B = 200 \,kg$.For piston $C$: $F_C = F_A 	imes \left(\frac{r_C}{r_A}ight)^2 = 2g 	imes \left(\frac{0.05}{0.1}ight)^2 = 2g 	imes (0.5)^2 = 2g 	imes 0.25 = 0.5g$.Thus, the mass that can be lifted by $C$ is $m_C = 0.5 \,kg$.The calculated masses are $200 \,kg$ and $0.5 \,kg$. Since this does not match any of the given options, the correct choice is $D$.

$A$ hydraulic lift is shown in the figure. The movable pistons $A, B$ and $C$ have radii of $10 \,cm, 100 \,cm$ and $5 \,cm$ respectively. If a body of mass $2 \,kg$ is placed on piston $A$, what are the maximum masses that can be lifted by pistons $B$ and $C$ respectively?

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