In a vehicles lifter, the enclosed gas exerts force F on a small piston of 8 cm diameter. The pressure is transmitted to a second piston of diameter 24 cm. If the mass of the vehicle to be lifted is 1400 kg, then F must at least be .. $(g = 10 {ms}^{- 2})$

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1200 N

1600 N

700 N

1000 N

answer is A.

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Detailed Solution

$Here, r_{1} = 4 cm and r_{2} = 12 cm$

$F_{1} = F and F_{2} = mg = 1400 \times 10 N$

According to pascal's law

$\begin{array}{r} F_{1} = F_{2} \times \frac{r_{1}^{2}}{r_{2}^{2}} = 14 \times 10^{3} \times {(\frac{4}{12})}^{2} \\ = 14 \times 10^{3} \times \frac{1}{9} ≅ 1600 N \end{array}$

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