Q103 / 110 · VITEEE 2024 · Physics

In a car lift, compressed air exerts a force $F_1$ on a small piston having a radius of 5.0 cm . This pressure is transmitted to a second piston of radius 10.0 cm . If the mass of the car to be lifted is 1350 kg . The force on a small piston is

  • Correct answer
    A
    1470 N
  • B
    1480 N
  • C
    1490 N
  • D
    1500 N

Solution

Here, $r_1=\frac{5}{100} \mathrm{~m}$, $F_2=1350 \mathrm{~kg}=1350 \times 9.8 \mathrm{~N}, r_2=\frac{10}{100} \mathrm{~m}$ According to Pascal law, As, $\frac{F_1}{A_1}=\frac{F_2}{A_2}$ or $F_1=\frac{A_1}{A_2} F_2=\frac{\pi r_1^2}{\pi r_2^2} F_2$ or $F_1=\frac{r_1^2}{r_2^2} F_2=\frac{\left(\frac{5}{100}\right)^2}{\left(\frac{10}{100}\right)^2} \times 1350 \times 9.8=1470 \mathrm{~N}$

Hence, the correct answer is option: 'A'.

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