A piston of cross-sectional are 100 cm² is used in a hydraulic press to exert a force of 10⁷ dyne on water. The cross-sectional area of the other piston which supports a truck of mass 200 kg is,

Given,

${\mathrm{F}}_1={10}^7\mathrm{dyne}=100\mathrm{N}$

${\mathrm{F}}_2=\left(200\times \mathrm{g}\right)\mathrm{N}$

${\mathrm{A}}_1=100{\mathrm{cm}}^2$

According to Pascal's law, a change in pressure at one piston causes the other piston to move.

${\mathrm{F}}_1/{\mathrm{A}}_1={\mathrm{F}}_2/{\mathrm{A}}_2$

${\mathrm{A}}_2=\frac{{\mathrm{F}}_2\times {\mathrm{A}}_1}{{\mathrm{F}}_1}$

${\mathrm{A}}_2=\frac{(200\times 9.8)\times (100\times {10}^{-4})}{100}=0.196{\mathrm{m}}^2$

Hence the correct answer is $0.196{\mathrm{m}}^2.$